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Patterns in sequences 2 | Linear equations | Algebra I | Khan Academy

Video vocabulary

another

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US / əˈnʌðə(r) /

UK / əˈnʌðɚ /

A1
  • adjecitve
  • One more, but not this
  • determiner
  • One more added
  • pronoun
  • One more (thing)

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

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

finally

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US / ˈfaɪnəli /

UK / ˈfaɪnəli /

A1
  • adverb
  • used especially at the beginning of a sentence to introduce the last point or idea
  • After a long time or some difficulty

forever

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US / fər'evə(r) /

UK / fɔrˈɛvɚ, fə- /

B1
  • adverb
  • For all future time; in the future

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

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

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

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

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

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
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

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

five

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US / faɪv /

UK / faɪv /

A1
  • number
  • 5

kind

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US / kaɪnd /

UK / kaɪnd /

A1
  • adjecitve
  • In a caring and helpful manner
  • friendly and considerate
  • noun
  • One type of thing

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?
  • (Used to ask someone or something's condition)

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

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

here

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

new

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US / nju: /

UK / nu, nju /

A1
  • adjecitve
  • Not old, recently born, built or made
  • Being or doing something for the first time
  • Not felt, seen or known previously
  • Having been recently bought or obtained

try

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US / traɪ /

UK / traɪ /

A1
  • noun
  • Act of putting the ball over the rugby goal line
  • verb
  • To make an effort, to attempt to do something
  • To examine someone or something in a court of law
  • To test to see if it is good or you like it
  • To make a person go through hardship; test
  • To examine something to see if it works

plus

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US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero

third

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US / θɜ:d /

UK / θɜ:rd /

A1
  • adjecitve
  • 3rd: Number after second

realize

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US / 'ri:əlaɪz /

UK / ˈriəˌlaɪz /

A1
  • verb
  • To become aware of or understand mentally

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

always

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US / 'ɔ:lweɪz /

UK / ˈɔlwez,-wɪz,-wiz /

A1
  • adverb
  • For a very long time
  • At all times; in every situation
  • For ever

many

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US / 'menɪ /

UK / ˈmɛni /

A1
  • determiner
  • Used to refer a large number of things

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

four

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US / fɔ:(r) /

UK / fɔr, for /

A1
  • number
  • 4

imagine

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US / ɪ'mædʒɪn /

UK / ɪˈmædʒɪn /

A1
  • verb
  • To think creatively about; form mental picture of

house

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US / haʊs /

UK / haʊs /

A1
  • noun
  • Place where a specific activity or business occurs
  • Building in which a family, person lives
  • verb
  • To give someone a place to live
  • To contain or store 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

down

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US / daʊn /

UK / daʊn /

A1
  • adjecitve
  • Being sad, sick, or unhappy
  • Not operating, working, or functioning as expected
  • adverb
  • In a sitting or lying position
  • Towards or on the ground, floor, or bottom
  • Written or copied onto a piece of paper or book
  • noun
  • A period of play in American Football
  • The soft, smooth hairs that cover a bird's body
  • preposition
  • Along something's path, course, or direction
  • Going from a higher position to a lower position
  • verb
  • To eat or drink very quickly and without stopping

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

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

sequence

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US / 'si:kwəns /

UK / ˈsikwəns, -ˌkwɛns /

A2
  • noun
  • Part of a movie showing one part of the story
  • verb
  • To arrange things in an order they should happen

mean

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US / mi:n /

UK / min /

A1
  • adjecitve
  • Being good at
  • Nasty; unkind
  • Not liking to spend money; cheap; stingy
  • noun
  • Average of a set of numbers
  • verb
  • To express a particular idea or thought
  • To intend to do something in particular
  • To have a particular meaning or value

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)

even

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US / 'i:vn /

UK / ˈivən /

A1
  • adjecitve
  • Being equal in influence, power, possibility etc.
  • Being divided equally or fairly
  • (Of teams/contest) with similar chances of success
  • Smooth, level, or regular
  • Can be divided by 2; ending in 2, 4, 6, 8, or 0
  • At a regular, equally steady manner
  • Remaining steady and unchanging
  • adverb
  • (When this is surprising) as well; too
  • (Used to compare two things/stress the difference)
  • verb
  • To make something level; to flatten
  • To make something equal

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

happen

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US / 'hæpən /

UK / ˈhæpən /

A1
  • verb
  • To take place or occur

fourth

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US / fɔ:θ /

UK / fɔ:rθ /

A1
  • noun
  • 4th

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

figure

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US / ˈfiɡə /

UK / ˈfɪɡjɚ /

A1
  • noun
  • Your body shape
  • Numbers in a calculation
  • Doll-like thing meant to represent a person
  • Picture or diagram giving information in a text
  • Person who is very important or famous
  • Shape of a person seen indistinctly or in outline
  • Amount that is expressed in numbers
  • verb
  • To appear in a game, play or event
  • To calculate how much something will cost
  • To understand after thinking; work out

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

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
  • Act of searching for or examining something
  • verb
  • To appear to be; seem

abstract

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US / 'æbstrækt /

UK / ˈæbˌstrækt /

B1
  • adjecitve
  • Concerning something that doesn't exist physically
  • noun
  • Passage of text from an article or book
  • Something that doesn't exist physically
  • Short summary of an academic article
  • verb
  • To take out or remove a part of
  • To summarize an academic article

everything

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US / 'evrɪθɪŋ /

UK / ˈɛvriˌθɪŋ /

A1
  • pronoun
  • All of the things mentioned

original

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US / ə'rɪdʒənl /

UK / əˈrɪdʒənəl /

A2
  • adjecitve
  • Being first made, thought or performed; fresh
  • Being unique or thinking differently from others

they

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US / ðeɪ /

UK / ðe /

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

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

take

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US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

ask

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US / ɑ:sk /

UK / æsk /

A1
  • verb
  • To say to someone that you want something

exact

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US / ɪɡ'zækt /

UK / ɪɡˈzækt /

A2
  • adjecitve
  • Completely correct; accurate; specific
  • verb
  • To get something, sometimes using force

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

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

extension

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US / ɪkˈstenʃn /

UK / ɪkˈstɛnʃən /

B1
  • adjecitve
  • Adding extra length
  • noun
  • Addition to something, e.g. a house
  • Suffix code of a computer file, e.g. .pdf, .jpg
  • Telephone for individual person, e.g. In an office
  • Something added to the end of something
  • Extra time allowed to complete something

for

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US / fə(r) /

UK / fɔr,fə /

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

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

why

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US / waɪ /

UK / hwaɪ, waɪ /

A1
  • adverb
  • Question word to ask for a reason
  • exclamation
  • (Used to express surprise or approval)

trace

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US / treɪs /

UK / tres /

B1
  • noun
  • Very small quantity of something
  • verb
  • To make an outline to determine a shape
  • To find someone or something that has disappeared
  • To draw the outline of an image through thin paper

green

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US / gri:n /

UK / ɡrin /

A1
  • adjecitve
  • Color of young leaves
  • Covered with vegetation, e.g. grass
  • Concerned about protecting the environment
  • The color of young leaves
  • Lacking in experience/knowledge due to being young
  • Being not fully grown or ripe, as in fruit
  • noun
  • Large grassy area
  • used as a part of a name of a place (UK)

object

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US / 'ɒbdʒɪkt /

UK / ˈɑbdʒɪkt /

A2
  • noun
  • Something you can see or touch, but is not alive
  • Goal or purpose of a particular plan or activity
  • The thing that the action of a verb acts upon
  • verb
  • To disagree; to protest against an idea or plan

question

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US / 'kwestʃən /

UK / ˈkwɛstʃən /

A1
  • noun
  • Issue or problems you are dealing with
  • What you ask about; issue
  • verb
  • To ask for or try to get information
  • To have or express concerns or uncertainty

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

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

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

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

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

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

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)

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

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

toothpick

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US / ˈtu:θpɪk /

UK / ˈtuθˌpɪk /

A1
  • noun
  • Small strip of wood, plastic used to clean teeth

business

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US / ˈbɪznəs /

UK / ˈbɪznɪs /

A1
  • noun
  • A company formed for making profit
  • Matter that has to be dealt with; task; situation
  • Activity of working to make a profit

pattern

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US / 'pætn /

UK / ˈpætən /

A2
  • noun
  • Model to follow in making or doing something
  • Colors or shapes which are repeated on objects
  • Regular repeated behavior
  • verb
  • To copy the way something else is made

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

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

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

same

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US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite
  • Subtitles section
  • Our question asks us, how many toothpicks will be needed to form the 50th figure in this sequence?
  • So let's look at this sequence.
  • So the first figure in our sequence-- they look like little houses-- how many toothpicks are here?
  • We have one, two, three, four, five, six toothpicks.
  • So our first object here, or our first figure, has six toothpicks.
  • How many do we have in our second figure?
  • Well we're going to have these six that we had in the first, right?
  • This is the first figure, right here.
  • Let me just trace it.
  • That's the first figure, right there.
  • And then how many new toothpicks are we going to have?
  • We have one, two, three, four, five.
  • So we have six plus another five.
  • So we have the six in the original one, plus another five, which is equal to 11 toothpicks.
  • Now what happens in this third object, or this third little toothpick house looking drawing thing?
  • So we have our figure from the two houses.
  • So we have those right there.
  • This is the exact same thing that we had as our second object.
  • So that's that right there.
  • And how many more do we have?
  • Well it's going to be the same thing.
  • We've just added on this other extension to our house.
  • You can view it that way.
  • So we have one, two, three, four, five.
  • So it looks like every time we go down this sequence, or we add a new term to the sequence, or a new object to the sequence, we're adding five toothpicks.
  • So here, we're going to have 11 plus 5.
  • There's 11 toothpicks in this part of it, and then we have another 5.
  • 11 plus 5, which is 16.
  • Same thing over here.
  • We have 16 in this part of the drawing.
  • That part of the drawing is going to be 16 toothpicks, if you draw all of that.
  • And then we're going to have another five right here.
  • So this is going to be 16 plus 5 or 21.
  • So how can we figure out how many toothpicks we're going to have in the 50th figure?
  • I mean, we could draw 50 of them, but it's going to take us forever.
  • So all we have to do is realize the pattern.
  • Every one, we're just going to add 5.
  • Or, we could even come up with a formula for the nth figure.
  • How many toothpicks in the nth figure?
  • So here, in the first figure, we have-- you could view it this way-- in this first figure, we have 1 plus 5 toothpicks.
  • Right?
  • We have this 1.
  • You could imagine that was always there, and then you added 5 right there.
  • So that's our first term in our sequence.
  • Our second term in our sequence, what do we have?
  • We have 6, which is 1 plus 5.
  • So we have that 1 plus 5, plus another 5.
  • Plus this 5 right here, plus another 5.
  • And then our third term in our sequence, what do we have?
  • We have all of this business that we had in the second term.
  • So 1 plus 5 plus 5, and then we have another 5.
  • Let me do it in green.
  • We have another 5.
  • And then, finally, in this fourth term, what do we have?
  • We have-- so the fourth one-- we have everything that we had in the third figure, so 1 plus 5 plus 5 plus 5.
  • And then we add another 5.
  • We add a fourth 5.
  • We add a fourth 5 right there.
  • So why did I do it this way?
  • Because I wrote this first one as 1 plus 5 instead of just a 6 because you could say, well look, I had a 1, and then I had one 5.
  • Now I have a 1, and I have two 5's.
  • Now I have a 1 and I have three 5's.
  • Now I have a 1 and I have four 5's.
  • So you might see the pattern.
  • If I had the nth term, if I had the nth term right here, I will have a 1 plus n 5's, right?
  • The first term has one 5.
  • The second term has two 5's.
  • Third term has three 5's.
  • Fourth term has four 5's.
  • So the nth term, if this is, you know, if this is 10, it's going to be 1 plus 10 5's.
  • Or if it's n, if I'm kind of abstracting a little bit, I'm going to have 1 plus 10-- sorry-- 1 plus 5 times n, right?
  • And try it out.
  • If n is equal 1, it's going to be 5 times 1.
  • If n is equal to 2, it's going to be 5 times 2.
  • If n is equal to 3, it's going to be 5 times 3.
  • So that when the 50th term, if we're talking about the 50th term, how many toothpicks are we going to have?
  • Well we're going to have 1 plus 5 times 50, right? n is 50 here, which is equal to what?
  • 5 times 50 is 250.
  • That's 250 and then we add 1, we're going to have 251 toothpicks will be needed to form the 50th figure in this sequence.