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Geometric series word problems: swing | Algebra 2 | Khan Academy

Video vocabulary

something

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US / ˈsʌmθɪŋ /

UK / ˈsʌmθɪŋ /

A1
  • adverb
  • In some degree or measure
  • noun
  • a person or thing of some value or consequence
  • pronoun
  • Thing that is not yet known or named
  • Approximately

come

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US / kʌm /

UK / kʌm /

A1
  • verb
  • To arrive at a place
  • (Of mail) to be delivered
  • To move toward someone; go with someone
  • To reach a certain point or state

distance

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US / 'dɪstəns /

UK / ˈdɪstəns /

A2
  • noun
  • Lack of friendliness toward another person
  • Amount of space between two places or things
  • verb
  • To make it clear that you are not involved

leave

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US / li:v /

UK / liv /

A1
  • noun
  • Permission to do something
  • Vacation time; time off work
  • verb
  • To go away from; depart
  • To gift property to someone after you die
  • To allow something to continue happening
  • To let something remain unused or available
  • To let something or someone remain somewhere

tree

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US / tri: /

UK / tri /

A1
  • noun
  • Tall green plants in a forest

where

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US / hwɛə /

UK / hwɛr, wɛr /

A1
  • conjunction
  • At or in the place which
  • In whatever place
  • pronoun
  • Word you use to ask the location of something

legitimate

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US / lɪ'dʒɪtɪmət /

UK / ləˈdʒɪtəmɪt /

B2
  • adjecitve
  • Being born to legally married parents
  • Being reasonable and sound
  • verb
  • To make acceptable and sound

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

back

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US / bæk /

UK / bæk /

A1
  • adjecitve
  • Farthest from the front e.g. in a classroom
  • adverb
  • Have returned to a place you were before
  • noun
  • The part of a chair that the upper body leans upon
  • Location at the rear of something
  • The reverse of side something
  • Area on the rear of your body
  • verb
  • To bet money on something
  • To go backwards in a car
  • To support and encourage someone or some cause

from

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US / frəm /

UK / frʌm, frɑm,frəm /

A1
  • preposition
  • Starting at a particular place, time or level

form

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US / fɔ:m /

UK / fɔrm /

A1
  • noun
  • Sports team or person's current winning record
  • Document you complete when making an application
  • Visible shape or style; type; kind
  • verb
  • To organize something such as a club or group
  • To develop; to come into a shape or substance
  • To make something into a particular shape

minus

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US / ˈmaɪnəs /

UK / ˈmaɪnəs /

A2
  • adjecitve
  • Being close to the bottom of a letter grade
  • noun
  • Negative quality; disadvantage
  • Sign that indicates subtraction
  • preposition
  • Being less than zero in number
  • Used when subtracting one number from another
  • verb
  • To take one number away from another; subtract

out

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US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

over

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US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

only

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US / ˈəunli /

UK / ˈonli /

A1
  • adverb
  • Just one; just that amount or thing; not more than
  • Not very important or serious
  • Just that type of thing, person
  • Short time ago; not before a certain time
  • conjunction
  • Except; but

put

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US / pʊt /

UK / pʊt /

A1
  • phrasal verb
  • to make a light stop shining by pressing or moving a switch
  • verb
  • To move or place a thing in a particular position
  • To rate something in importance or value
  • To write or say something in a certain manner

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

meter

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US / ˈmi:tə(r) /

UK / ˈmitɚ /

A1
  • noun
  • Unit of length equal to 100 cm or about 39 inches
  • Device for measuring things e.g. gas
  • Device to put money into to rent a parking place
  • Rhythm of a poem
  • verb
  • To measure water, etc. when it has to be paid for

draw

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US / drɔ: /

UK / drɔ /

A1
  • noun
  • Something that attracts people to visit a place
  • A lottery or prize
  • Result of a game, contest where the score is equal
  • verb
  • To attract attention to someone or something
  • To get closer to or approach something or someone
  • To influence a person's involvement in something
  • To move an object by pulling
  • To create an image using pen or pencil and paper
  • To take one thing out of a container, etc.
  • (Of 2 teams) to finish a game with the same score

notice

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US / 'nəʊtɪs /

UK / ˈnotɪs /

A1
  • noun
  • Time by when you must leave, e.g. if you are fired
  • Paper with an announcement, e.g. pinned to a board
  • verb
  • To become aware by sight, touch, or hearing

choice

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US / tʃɔɪs /

UK / tʃɔɪs /

A1
  • adjecitve
  • Of good quality or taste; desirable
  • noun
  • Decision between two or more possibilities

negative

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US / 'neɡətɪv /

UK / ˈnɛɡətɪv /

A2
  • adjecitve
  • Being harmful, unwanted or unhelpful
  • In mathematics, being less than zero
  • Focusing on the bad aspects; pessimistic
  • noun
  • The opposite to a positive electrical charge
  • In grammar, containing words such as 'no' or 'not'
  • Reply to a question or statement that means 'no'
  • Image on camera film used to make a photo

see

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US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)

complete

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US / kəm'pli:t /

UK / kəmˈplit /

A1
  • adjecitve
  • Being finished; done; achieved
  • Being as perfect and as total as could be
  • verb
  • To finish or reach the end of doing something

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

know

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US / nəʊ /

UK / noʊ /

A1
  • verb
  • To be familiar with a person or place, thing
  • To feel sure or be convinced about something
  • To discover or be aware of something
  • To be able to distinguish
  • To have knowledge of things

with

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US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

have

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US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

last

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US / lɑ:st /

UK / læst /

A1
  • adjecitve
  • Most recent; the latest
  • The one before
  • adverb
  • Final; with nothing following; after all others
  • Most recent; the latest
  • determiner
  • The one at the end
  • verb
  • To remain or continue for a certain period of time

part

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US / pɑ:t /

UK / pɑ:rt /

A1
  • adjecitve
  • To some degree; half; not fully
  • noun
  • Division of a book
  • Ratio of something, e.g. 3 of gin, 1 of tonic
  • A line in a person's hair, made with a comb
  • Character an actor plays on stage, movie, or TV
  • Some, but not all of a specific thing
  • Role in causing something to happen
  • verb
  • To make a line in a person's hair, by using a comb
  • To move two things apart creating a space
  • To leave someone, or to break off a relationship

six

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US / sɪks /

UK / sɪks /

A1
  • number
  • 6

next

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US / nekst /

UK / nɛkst /

A1
  • adverb
  • The one that follows another in time or order
  • At a time or place directly after the present one
  • noun
  • The one that follows after
  • adjecitve
  • Immediately after the previous one
  • First occurrence after the present one

exponent

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US / ɪkˈspəʊnənt /

UK / ɪkˈsponənt, ˈɛkˌsponənt /

C1
  • noun
  • Person who exemplifies an art movement, etc.

remember

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US / rɪ'membə(r) /

UK / rɪˈmɛmbɚ /

A1
  • verb
  • To give someone a gift, e.g. birthday, wedding
  • To hold a thought in your mind to not forget it
  • To bring a previous image or idea to your mind

ratio

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US / ˈreɪʃiəʊ /

UK / ˈreɪʃioʊ /

C2
  • noun
  • The relationship in relative size, etc.

would

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US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

prediction

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US / prɪˈdɪkʃn /

UK / prɪˈdɪkʃən /

A2
  • noun
  • A statement of what will happen next

round

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US / raʊnd /

UK / raʊnd /

A1
  • adjecitve
  • Being in the shape of a circle or ball
  • Consisting of curved and not straight lines
  • Somewhat fat or curved in physical appearance
  • Being a whole number, not a fraction, decimal
  • adverb
  • From beginning to end (e.g. of the year)
  • noun
  • One of the three-minute periods in boxing
  • Drinks bought by one person for a group
  • Series regular visits, routes, or stops at places
  • Single shot or bullet fired from a gun
  • An object with a circular shape
  • One stage in a series of games, e.g. football
  • One's turn in a game such as cards
  • preposition
  • Going around
  • verb
  • To cause or make a circular or curved shape
  • To go or pass around the bend or corner
  • To change from a fraction to nearest whole number

sense

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US / sens /

UK / sɛns /

A1
  • noun
  • Certain mental feeling or emotion
  • Normal or clear state of mind
  • Meaning of a particular word, phrase or text
  • verb
  • To perceive using sight, sound, taste touch etc.
  • To recognize the presence of something

sum

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US / sʌm /

UK / sʌm /

A2
  • noun
  • Amount when all is added together; total
  • verb
  • To add two or more numbers together; total

want

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US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

video

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US / 'vɪdɪəʊ /

UK / ˈvɪdiˌo /

A2
  • adjecitve
  • Of a moving film, with sound
  • noun
  • Recording capturing action with sound
  • verb
  • To make a moving film of, with sound

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

experience

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US / ɪk'spɪərɪəns /

UK / ɪkˈspɪriəns /

A1
  • noun
  • Thing a person has done or that happened to them
  • An event at which you learned something
  • Knowledge gained by living life, doing new things
  • verb
  • To gain knowledge by doing things

formula

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US / 'fɔ:mjələ /

UK / ˈfɔrmjələ /

A2
  • noun
  • A mathematical or scientific rule
  • Plan, rule or method for doing or making something

equal

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US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

maybe

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US / ˈmeɪbi /

UK / ˈmebi /

A1
  • adverb
  • Possibly but not certainly; perhaps

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

final

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US / ˈfaɪnl /

UK / ˈfaɪnəl /

A1
  • adjecitve
  • That will not be changed; permanent
  • Being the last thing in a series
  • noun
  • Last game in a series in a competition

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

give

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US / ɡɪv /

UK / ɡɪv /

A1
  • noun
  • Degree of flexibility in something, a material
  • verb
  • To hand over or present something to someone
  • To cause someone to have or experience something

total

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US / ˈtəʊtl /

UK / ˈtoʊtl /

A1
  • adjecitve
  • Complete
  • noun
  • Whole number or amount of something
  • verb
  • To damage a car beyond repair

first

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US / fɜ:st /

UK / fɚst /

A1
  • adjecitve
  • 1st; Coming before all others in time or place
  • noun
  • Something that has not happened before
  • Position of the winner of a competition

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

hint

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US / hɪnt /

UK / hɪnt /

A2
  • noun
  • Helpful piece of information
  • Tiny quantity or sign of something
  • verb
  • To suggest without being direct about it

interesting

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US / ˈɪntrəstɪŋ /

UK / ˈɪntrɪstɪŋ, -tərɪstɪŋ, -təˌrɛstɪŋ /

A1
  • adjecitve
  • Taking your attention; making you want to know
  • verb
  • To make someone want to know about something
  • To persuade to do, become involved with something

number

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US / ˈnʌmbə(r) /

UK / ˈnʌmbɚ /

A1
  • noun
  • Symbols such as 1, 2, 56, 793
  • Particular song or dance performed during a show
  • Total quantity or amount of things
  • verb
  • To put numbers on things
  • To assign a sequence within a group, series, set
  • To claim to be part of a larger group, series, set

tell

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US / tel /

UK / tɛl /

A1
  • verb
  • To (strongly) advise a person to do something
  • To be able to guess
  • To say or communicate information to someone
  • To inform, but without speaking; indicate
  • To have a negative effect on someone
  • To order someone to do something; command
  • To recognize something based on certain signs
  • To report something to an authority
  • To explain something or teach someone something

right

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US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

she

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US / ʃɪ /

UK / ʃi /

A1
  • pronoun
  • Female person or animal mentioned before
  • (Refers to female person mentioned before)

swing

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US / swɪŋ /

UK / swɪŋ /

A2
  • noun
  • Movement in a curved motion
  • Flowing, curved movement, e.g. of the arm
  • A back and forth motion, while hanging
  • Change in opinion or theme
  • Outdoor seat that hangs by two ropes, or chains
  • verb
  • To move something in a back and forth motion
  • To move in a back and forth motion, while hanging
  • To change opinion or mood, usually quickly

include

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US / ɪnˈklu:d /

UK / ɪnˈklud /

A1
  • verb
  • To make someone, something part of a group

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

about

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US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

like

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US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

second

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US / 'sekənd /

UK / ˈsɛkənd /

A1
  • adjecitve
  • 2nd; the one following first
  • noun
  • Unit of time; one sixtieth of a minute
  • Short period of time that you wait for someone
  • (Do) soon

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

what

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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

arc

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US / ɑ:k /

UK / ɑrk /

B2
  • noun
  • Smoothly curving line or movement
  • verb
  • To bend in a smooth curve

each

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US / i:tʃ /

UK / itʃ /

A1
  • determiner
  • Every one of two or more things
  • pronoun
  • Per one person or thing

nth

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US / enθ /

UK / ɛnθ /

C2
  • number
  • Last or greatest in an indefinitely large series

term

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US / tɜ:m /

UK / tɚm /

A1
  • noun
  • Conditions applying to an agreement, contract
  • Length of time something is expected to happen
  • Fixed period of weeks for learning at school
  • The (precise) name given to something
  • verb
  • To call; give a name to

three

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US / θri: /

UK / θri /

A1
  • number
  • Number 3

little

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US / 'lɪtl /

UK / ˈlɪtl /

A1
  • adjecitve
  • Being short in length of time
  • Not great in size, amount, or degree; small
  • Being very young or younger than others
  • adverb
  • By an amount or degree that is not very much
  • Not often; rarely
  • noun
  • A person's name

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

might

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US / maɪt /

UK / maɪt /

A1
  • other
  • Used to politely request an action
  • Used to express that something could happen
  • Power, strength, force or influence

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

half

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US / hɑ:f /

UK / hæf, hɑf /

A1
  • adjecitve
  • Not complete
  • adverb
  • Partly; somewhat
  • noun
  • One of two equal periods of game time in a sport
  • The part you get when one is divided into two;

one

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US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

other

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US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

power

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US / 'paʊə(r) /

UK / ˈpaʊɚ /

A1
  • noun
  • Legal or official right to perform certain actions
  • Ability to move forcefully and quickly
  • Energy of something (e.g. electricity or fuel)
  • Mathematical way to multiply a number
  • Condition of being in political control
  • Physical force, energy, and strength
  • verb
  • To give energy to something, e.g. by electricity
  • To move something forcefully and quickly

also

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US / 'ɔ:lsəʊ /

UK / ˈɔlso /

A1
  • adverb
  • In addition; too; in a similar way

how

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US / haʊ /

UK / haʊ /

A1
  • adjecitve
  • To what degree? in what amount?
  • adverb
  • (Used to explain the way to do something)
  • exclamation
  • For what purpose or reason?
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you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
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this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
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  • determiner
  • Person, thing, or idea near you
  • pronoun
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answer

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US / 'ɑ:nsə(r) /

UK / ˈænsɚ /

A1
  • noun
  • Reply to a question someone asks
  • Solution to a problem or test question
  • verb
  • To reply to a question someone asks
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predict

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US / prɪ'dɪkt /

UK / prɪˈdɪkt /

A2
  • verb
  • To guess or estimate what will or might happen

make

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US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
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  • To cause something to happen or be formed

bit

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US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

look

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US / lʊk /

UK / lʊk /

A1
  • noun
  • Person's beauty or physical attractiveness
  • Particular style of dress, clothes, or appearance
  • The way someone, something appears to be
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  • verb
  • To appear to be; seem

multiply

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US / ˈmʌltɪplaɪ /

UK / ˈmʌltəˌplaɪ /

B1
  • verb
  • To increase in number by reproducing/having babies
  • To increase something by a large quantity
  • To have increased by a large quantity
  • To calculate two numbers e.g. 2 x 4

all

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US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

common

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US / 'kɒmən /

UK / ˈkɑmən /

A1
  • adjecitve
  • Shared; Belonging to or used by everyone
  • Typical, normal; not unusual
  • noun
  • Area in a city or town that is open to everyone
  • Field near a village owned by the local community

successive

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US / səkˈsesɪv /

UK / səkˈsɛsɪv /

B2
  • adjecitve
  • Happening one after another in a series

top

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US / tɒp /

UK / tɑp /

A1
  • adjecitve
  • Being good or great; excellent
  • Being the most in degree or quality
  • noun
  • Item of clothing covering shoulders to waist, hips
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  • verb
  • To be higher or larger than a specific value
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  • To kill; murder
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who

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US / hu: /

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A1
  • pronoun
  • Which person
  • Used to introduce information about people

expression

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US / ɪk'spreʃn /

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A2
  • noun
  • Act of making your thoughts and feelings known
  • Group of words that have a specific meaning

length

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US / leŋθ /

UK / leŋθ /

A2
  • noun
  • Distance from one end of a pool to the other
  • Measurement of distance or of time

pretty

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US / 'prɪtɪ /

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A1
  • adjecitve
  • Being attractive to the eye in a simple way
  • adverb
  • Very; to a great degree

subtract

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US / səbˈtrækt /

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B2
  • other
  • To take away a value or amount from another
  • verb
  • To take away a value or amount from another

vine

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US / vaɪn /

UK / vaɪn /

B2
  • noun
  • Long thin plant that climbs over something

both

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US / bəuθ /

UK / boθ /

A1
  • determiner
  • Used to refer to two things at the same time
  • pronoun
  • Used to refer to two things at the same time

hold

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US / həʊld /

UK / hold /

A1
  • noun
  • Section of a ship or plane used for storing things
  • Influence or power held over someone
  • Place of support for hands or feet when climbing
  • verb
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  • To have a specific quality or property
  • To keep an image, belief or feeling in your mind
  • To have or own something
  • To wait before being able to talk on the phone
  • To limit the movement of someone in a sport

travel

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US / ˈtrævl /

UK / ˈtrævəl /

A1
  • noun
  • Going to other places, esp. distant places
  • verb
  • To go to a place that is far away

way

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US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

prove

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US / pru:v /

UK / pruv /

A2
  • verb
  • To demonstrate truth by providing evidence

work

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US / wɜ:k /

UK / wɚk /

A1
  • adjecitve
  • Activity completed in order to make money
  • noun
  • The product of some artistic or literary endeavor
  • Everything created by an author, artist, musician
  • Activity you do in order to make money
  • Place of employment
  • Final product or result of a some labor or effort
  • verb
  • To bring into a specific state of success
  • To be functioning properly, e.g. a car
  • To do your job in your company or workplace
  • To make an effort to do something
  • To operate a machine or device

they

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US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

very

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US / 'verɪ /

UK / ˈvɛri /

A1
  • adjecitve
  • Concerning a large degree or amount
  • adverb
  • A lot; much; many
  • Used to stress or emphasize a noun

add

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US / æd /

UK / æd /

A1
  • verb
  • To include as well
  • To put two things or numbers together, e.g. 2+2

calculator

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US / 'kælkjʊleɪtə(r) /

UK / ˈkælkjəˌletɚ /

B2
  • noun
  • A small electronic device used for calculation

situation

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US / ˌsɪtʃuˈeɪʃn /

UK / ˌsɪtʃuˈeʃən /

A1
  • noun
  • Place, position or area that something is in
  • Circumstance or condition surrounding an event
  • An unexpected problem or difficulty

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

talk

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US / tɔ:k /

UK / tɔk /

A1
  • noun
  • Style of speaking
  • Discussion between two countries
  • Giving information in front of people; lecture
  • Saying things or ideas to someone with words
  • verb
  • To make a formal speech about something
  • To say things or ideas to someone with words

express

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US / ɪk'spres /

UK / ɪkˈsprɛs /

A1
  • adjecitve
  • Sent by a fast mail service
  • Traveling at high speed
  • noun
  • Fast train or bus
  • verb
  • To send something by fast mail
  • To state or show what you think or how you feel

pause

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US / pɔ:z /

UK / pɔz /

A2
  • noun
  • A temporary break before continuing
  • Function on a device to stop and restart it
  • Sign to hold a musical note a bit longer
  • verb
  • To stop doing for a while before continuing

well

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US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

finite

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US / ˈfaɪnaɪt /

UK / ˈfaɪˌnaɪt /

B1
  • adjecitve
  • Having limits; lasting for a limited time

for

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US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

through

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US / θru: /

UK / θru /

A2
  • adjecitve
  • having finished using or doing something
  • adverb
  • From the beginning of something until the end
  • preposition
  • Over, in, across an entire thing or place
  • Allowing you to pass between, or to
  • By a particular way or process; by the use of

time

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US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

those

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US / ðəʊz /

UK / ðoz /

A1
  • determiner
  • The people or things we are talking about
  • pronoun
  • The objects far from the speaker

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

use

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US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
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  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

write

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US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

equivalent

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US / ɪˈkwɪvələnt /

UK / ɪˈkwɪvələnt /

B1
  • adjecitve
  • Equal to something in value, use or meaning
  • noun
  • Thing like another in quality, quantity or degree

previous

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US / ˈpri:viəs /

UK / ˈpriviəs /

A2
  • adjecitve
  • Existing or happening before the present time

after

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US / 'ɑ:ftə(r) /

UK / ˈæftɚ /

A1
  • adverb
  • Later than another time, or behind something
  • conjunction
  • Following something before
  • preposition
  • When an event happened or time has passed

already

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US / ɔ:lˈredi /

UK / ɔlˈrɛdi /

A1
  • adverb
  • Having happened or been done before this time

geometric

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US / ˌdʒi:əˈmetrɪk /

UK / ˌdʒiəˈmɛtrɪk /

B2
  • adjecitve
  • With regular mathematical patterns/straight lines

will

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US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

true

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US / tru: /

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A1
  • adjecitve
  • Agreeing with the facts; not false; real or actual

explain

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US / ɪk'spleɪn /

UK / ɪkˈsplen /

A1
  • verb
  • To make clear or easy to understand by describing

either

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US / ˈaɪðə(r) /

UK / ˈiðɚ, ˈaɪðɚ /

A1
  • adjecitve
  • One of two (used when there is a choice of two)
  • adverb
  • (After negative statements) likewise, in addition
  • conjunction
  • Used as the first of two connected things
  • determiner
  • Used as the first of two connected things
  • pronoun
  • The one or the other

here

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US / hɪə(r) /

UK / hɪr /

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  • adverb
  • In this place; at this location, position or time

small

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US / smɔ:l /

UK / smɔl /

A1
  • adjecitve
  • Little in size; not big
  • (Of letters) not written in capital letters
  • Being insignificant or minor
  • (Of a business) with few people or things; local
  • (Of voice) being soft and quiet
  • (Of a child) being young

series

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US / ˈsɪəri:z /

UK / ˈsɪriz /

A1
  • noun
  • Set of stories or articles on a particular subject
  • other
  • Number of things that happen one after another

divide

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US / dɪ'vaɪd /

UK / dɪˈvaɪd /

A2
  • verb
  • To split numbers by another number, e.g. 6 / 2 = 3
  • To separate something into equal pieces
  • Introduction to Video Content
  • In this video, we will be discussing a word problem involving a monkey swinging from a tree. The problem states that on the first swing, the monkey passes through an arc of 24 meters. With each swing, the monkey passes through an arc that is one half the length of the previous swing. To visualize this, imagine a monkey swinging from the top of a rope or vine. On the first swing, the monkey would travel a distance of 24 meters. On the next swing, the monkey would swing back at an arc half the length of the previous swing, which would be 12 meters. Similarly, on the following swing, the monkey would swing half of that distance, which would be 6 meters. This pattern continues, with each swing having an arc length that is half the length of the previous swing. The question asks us to determine the total length the monkey swings in her first n swings. This can be expressed as a geometric series, where the common ratio is half. The expression can also be evaluated as the sum of a geometric series. By applying this information, we can calculate the total length the monkey swings in her first n swings.
  • Subtitles section
  • We're told a monkey is swinging from a tree.
  • On the first swing, she passes through an arc of 24 meters.
  • With each swing, she passes through an arc one half the length of the previous swing.
  • So what's going on here, let's say this is the top of the rope or the vine that the monkey is swinging from.
  • And so on that first swing, I could draw a little monkey here.
  • So this is my little monkey.
  • So on that first swing, the monkey will go 24 meters.
  • So might do something like this.
  • Then that arc is 24 meters.
  • And then on the second swing, it would be, she'd swing back at an arc half the length of the previous swing.
  • So then she would come back, and then it would be half the length.
  • And so maybe swing back over here.
  • And then on the next, so that would be 12. And then on the next swing, she would swing half of that, which would be six meters.
  • And so she might swing like this.
  • And that makes sense, that's consistent with our experiences swinging from trees, for those of us who've done that.
  • So let's look at the first choice.
  • Which expression gives the total length the monkey swings in her first n swings?
  • So pause the video and see if you can do that.
  • And you can express it as, actually express it both two ways.
  • Express it as a geometric series, but also express it as the sum of a geometric series if we were to actually evaluate it.
  • So let's do this together.
  • So we already said on the first swing, the monkey goes 24 meters.
  • Now on the second swing, and I gave you a hint when I said to express it as a geometric series, she swings half that.
  • Now I could just write a 12 here, but the half is interesting, because that's going to be my common ratio for my geometric series.
  • Every successive swing, the arc length is half the arc length of the last swing.
  • So it's going to be 24 times 1 1⁄2.
  • And then on the next swing, it's going to be 24, it's going to be half of this.
  • So it's going to be 24 times 1 1⁄2 times 1 1⁄2.
  • So that's 24 times 1 1⁄2 to the second power.
  • And so this would be the first three swings.
  • Notice that the exponent here, we got to the second power.
  • So the first n swings, we are going to get to 24 times 1 1⁄2, not to the nth power, but to the n minus one power.
  • Notice after two swings, we only get to 24 times 1 1⁄2 to the first power, after three swings to the second power.
  • So after n swings to the n minus one power.
  • Now, as I said, we don't want to just have this expression.
  • We actually want to know, how do we evaluate this?
  • And the way we evaluate this is we look at the formula, which we've explained and we've proven in other videos, the formula for a finite geometric series.
  • So that tells us, and I'll just write it over here, the sum of first, First n terms is a, where a is the first term, so that's going to be our 24 in this situation.
  • It's a minus a times our common ratio.
  • I already said that our common ratio is 1 1⁄2 to the nth power.
  • So one way I like to remember it is, it is our first term minus the first term that we didn't include, or minus what would have been the term right after this.
  • All of that over one minus our common ratio.
  • And there's other ways that you might have seen this written.
  • You could factor an a out, and you might have seen something like this, a times one minus r to the n, all of that over one minus r.
  • These two are equivalent.
  • But now, let's use this.
  • So this is going to be equal to, actually, I'll use this second form right over here.
  • So our first term, a, is 24. So we're going to have 24 times one minus our common ratio, which is 1 1⁄2 to the nth power.
  • Well, we're talking about the first n swing, so I'm just going to leave an n right over there.
  • All of that over one minus our common ratio, one minus 1 1⁄2.
  • So we could leave it like that, or we could simplify it a little bit if we like.
  • One minus 1 1⁄2 is equal to 1 1⁄2.
  • 24 divided by 1 1⁄2 is equal to 48. So if you wanted to, you could simplify it to 48 times one minus 1 1⁄2 to the nth power.
  • So either of these would be legitimate.
  • Now, the second part, they say, what is the total distance the monkey has traveled when she completes her 25th swing?
  • And they say, round your final answer to the nearest meter.
  • So pause this video and see if you can work that out.
  • All right, well, we can just use this expression here, and we know that we are completing our 25th swing.
  • So n is 25, and so we'll just put a 25 there.
  • So that's going to be 48 times one minus 1 1⁄2 to the 25th power.
  • Now, this is going to be a very, very small, very, very small number.
  • So it's actually going to be pretty close to 48 meters, but let's see what this is equal to, and we're going to round to the nearest meter.
  • All right, so let's get our calculator out.
  • And so let's just evaluate 1 1⁄2.
  • I'll just write that as 0.5 to the 25th power, which, as we said, as we predicted, is a very small number.
  • And then we're going to subtract that from one.
  • So let's put a negative, and then I'll add one to it.
  • And so that is very close to one, and so my prediction is holding true.
  • So if I multiply that times 48, well, if we round to the nearest meter, we get back to 48 meters.
  • So this is going to be 48 meters.
  • And we're done.