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Inductive reasoning 1 | Sequences, series and induction | Precalculus | Khan Academy

Video vocabulary

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

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

deal

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US / di:l /

UK / dil /

A1
  • verb
  • To cope with something - usually troubles
  • To give (something bad e.g. news) to
  • To buy and sell illegal drugs
  • To give out (cards, etc.) to; distribute
  • To do business with someone or to sell products

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

maybe

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US / ˈmeɪbi /

UK / ˈmebi /

A1
  • adverb
  • Possibly but not certainly; perhaps

increment

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US / 'ɪŋkrəmənt /

UK / ˈɪnkrəmənt, ˈɪŋ- /

B2
  • noun
  • Amount by which something is increased

distribute

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US / dɪˈstrɪbju:t /

UK / dɪˈstrɪbjut /

A2
  • verb
  • To hand out or give to people
  • To send products to stores to sell
  • To spread something over an area

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

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

num

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US / nʌm /

UK / en juː em /

A1
  • abbreviation
  • Numbers (in biblical references).

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

sure

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US / ʃʊə(r) /

UK / ʃʊr /

A1
  • adjecitve
  • Having no doubts about something
  • Have confidence in your own words or actions
  • Firmly established or held; being firm or stable
  • Being correct or true
  • adverb
  • What you say to agree willingly

third

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US / θɜ:d /

UK / θɜ:rd /

A1
  • adjecitve
  • 3rd: Number after second

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

here

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US / hɪə(r) /

UK / hɪr /

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

continue

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US / kən'tɪnju: /

UK / kənˈtɪnju /

A1
  • verb
  • To do something without stopping, or after pausing
  • To start doing again after a break, pause, or stop

think

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US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

any

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US / 'enɪ /

UK / ˈɛni /

A1
  • adjecitve
  • One, or some, no matter which
  • pronoun
  • One (thing) of many; some

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

keep

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US / ki:p /

UK / kip /

A1
  • noun
  • Large, strong tower in the middle of a castle
  • Money spent on you so you can live in a place
  • verb
  • To continue doing something; not to stop
  • To stop balls going in a goal in sports
  • To not give back or return something
  • (Of food) to not spoil or not rot
  • To take possession of something to own, e.g. a pet
  • To have and continue to hold something
  • To do something that you have promised or agreed
  • To stay in a certain place or condition
  • To maintain the rules

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

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

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

from

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US / frəm /

UK / frʌm, frɑm,frəm /

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

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

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)

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

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)

start

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US / stɑ:t /

UK / stɑrt /

A1
  • noun
  • First time or place that a thing exists; beginning
  • First opportunity to achieve something, e.g. a job
  • Sudden action or movement because you are scared
  • other
  • Beginning of something in place or time
  • verb
  • To do, be or happen for the first time; begin
  • To turn something on

since

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US / sɪns /

UK / sɪns /

A1
  • adverb
  • At a point before the present time
  • conjunction
  • For this reason; because
  • preposition
  • From the time in the past that

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

for

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US / fə(r) /

UK / fɔr,fə /

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

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

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

than

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US / ðən /

UK / ðən /

A1
  • conjunction
  • Used to compare two things that are not equal

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

level

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US / 'levl /

UK / ˈlɛvəl /

A2
  • adjecitve
  • (Sports) equal to another
  • Being steady and determined (e.g. a voice)
  • noun
  • Specific height of something
  • Amount of ability you have compared to others
  • Floor or deck within a building
  • Tool used to determine if something is lying flat
  • verb
  • To aim a gun at someone
  • To destroy a building; flatten an area completely
  • To make things flat or even
  • To make a score equal to another, in sports

you

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US / jʊ /

UK / ju /

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

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

multiple

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US / ˈmʌltɪpl /

UK / ˈmʌltəpəl /

B1
  • adjecitve
  • Having or involving more than one of something
  • noun
  • Number produced by multiplying a smaller number
  • Shop with many branches

nth

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US / enθ /

UK / ɛnθ /

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

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

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
  • To cause or force a person to do something
  • To cause something to happen or be formed

follow

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US / ˈfɔləu /

UK / ˈfɑlo /

A1
  • verb
  • To come after someone; be guided by someone
  • To support someone, e.g. singer or comedian
  • To be the logical result of something
  • To happen after something else happens
  • To believe a set of values or a moral teacher
  • To understand something happening or being said

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
  • verb
  • To agree to support a proposal at a meeting

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

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

value

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US / 'vælju: /

UK / ˈvælju /

A1
  • noun
  • Importance you attach to something
  • Some information expressed as a number
  • Stated price of something; worth
  • verb
  • To place a high importance on something
  • To say how much money something is worth

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

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

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

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

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

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’

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

again

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US / ə'ɡen /

UK / əˈɡɛn /

A1
  • adverb
  • One more time, once more

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)

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

expression

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US / ɪk'spreʃn /

UK / ɪkˈsprɛʃən /

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

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

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

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

general

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US / 'dʒenrəl /

UK / ˈdʒɛnərəl /

A1
  • adjecitve
  • Widespread, normal or usual
  • noun
  • Top ranked officer in the army

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

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

fourth

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US / fɔ:θ /

UK / fɔ:rθ /

A1
  • noun
  • 4th

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

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

they

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US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things
  • Subtitles section
  • What is the nth number in the following sequence?
  • Let's see.
  • The first term here is a 6.
  • So over here I'll put the term.
  • So this is the number.
  • I'll just write num there.
  • That's the number.
  • And this is the term.
  • So the first term here is a 6.
  • It looks like we add 3 to that to get to a 9.
  • Or maybe there's some other pattern here.
  • So that's the second term, is 9.
  • Then they go from 9 to 12.
  • Looks like we add 3 again.
  • So we keep adding 3.
  • So the third term is 12, the fourth term is 15.
  • And we need to think of a general expression that will give us the value of the nth term.
  • The nth number in the following sequence.
  • So let's think a little bit about it.
  • We know that we're incrementing by 3 every time and we're starting at 6.
  • So let's write these in terms of multiples of 3, since we know that that's the increment level.
  • This first term right here is 3 times 2.
  • The second term right here is 3 times 3.
  • This third term is 3 times 4.
  • And so it looks like it's 3 times one more than the actual term you are dealing with.
  • Right?
  • Here, if you take your term, you add 1 and then multiply that by 3, you get 6.
  • Take your term, add 1, then multiply it by 3.
  • Take your term, add 1, you get 4.
  • Then multiply by 3.
  • Take your term, add 1-- which would be 5-- and then multiply by 3, you get 15.
  • So it looks like any time-- so if you have your nth term.
  • So if you go all the way out here to your nth term, the value here would be you'd add 1 to it.
  • So you'd have n plus 1, and then you'd multiply that by 3.
  • So the nth term is 3 times n plus 1.
  • Or if you wanted to distribute out the 3, it'd be 3n plus 3.
  • And just make sure that works for all of them.
  • The first term, 3 times 1 is 3 plus 3, that works.
  • That's 6.
  • The second term, 3 times 2 plus 3 is 9.
  • So it works for all of these terms. So that is the nth term.
  • We have to assume that this pattern continues.