Subtitles section
Repeat sentence
Subtitles mode
Full screen
Previous
Next
x 1.0
Playback speed
More

Inductive reasoning 2 | Sequences, series and induction | Precalculus | Khan Academy

Video vocabulary

continue

Copy vocabulary

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

someone

Copy vocabulary

US / ˈsʌmwʌn /

UK / ˈsʌmˌwʌn, -wən /

A1
  • pronoun
  • Person who is not known or named

weird

Copy vocabulary

US / wɪəd /

UK / wɪrd /

B1
  • adjecitve
  • Odd or unusual; surprising; strange

true

Copy vocabulary

US / tru: /

UK / tru: /

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

use

Copy vocabulary

US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • 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

always

Copy vocabulary

US / 'ɔ:lweɪz /

UK / ˈɔlwez,-wɪz,-wiz /

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

guess

Copy vocabulary

US / ɡes /

UK / ɡɛs /

A1
  • noun
  • Answer given when you don't know if it is correct
  • verb
  • To give an answer without knowing if it is correct

will

Copy vocabulary

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

reason

Copy vocabulary

US / 'ri:zn /

UK / ˈrizən /

A1
  • noun
  • Ability to think about facts and form a judgment
  • Explanation for why something occurred or was done
  • verb
  • To think and make conclusions in a logical manner

sure

Copy vocabulary

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

Copy vocabulary

US / θɜ:d /

UK / θɜ:rd /

A1
  • adjecitve
  • 3rd: Number after second

could

Copy vocabulary

US / kəd /

UK / kʊd /

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

know

Copy vocabulary

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

induce

Copy vocabulary

US / ɪn'dju:s /

UK / ɪnˈdus, -ˈdjus /

B1
  • verb
  • To make someone do something; create an outcome
  • To make a woman give birth by giving her medicine

next

Copy vocabulary

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

see

Copy vocabulary

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)

have

Copy vocabulary

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

with

Copy vocabulary

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

completely

Copy vocabulary

US / kəmˈpli:tli /

UK / kəmˈpliːtli /

A1
  • adverb
  • In every way or as much as possible

minus

Copy vocabulary

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

keep

Copy vocabulary

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

something

Copy vocabulary

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

far

Copy vocabulary

US / fɑ:(r) /

UK / fɑr /

A1
  • adjecitve
  • A long way away
  • Being a long way away
  • adverb
  • To a large degree or extent

think

Copy vocabulary

US / θɪŋk /

UK / θɪŋk /

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

proposition

Copy vocabulary

US / ˌprɒpəˈzɪʃn /

UK / ˌprɑ:pəˈzɪʃn /

B1
  • noun
  • General claim or theory
  • Something you want to do that may be difficult

and

Copy vocabulary

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

base

Copy vocabulary

US / beɪs /

UK / bes /

A2
  • noun
  • Place military personnel live, train, and operate
  • Bottom part of an object that touches a surface
  • Unit of counting, e.g. 10 for counting
  • Most important idea or ingredient to add others
  • Origin or start from which something came
  • Main place where an organization or a person works
  • verb
  • To use as the starting point or origin for
  • To have as the main location for (company, etc.)

just

Copy vocabulary

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)

necessarily

Copy vocabulary

US / ˌnesəˈserəli /

UK / ˌnɛsɪˈsɛrəli, -ˈsɛr- /

A2
  • adverb
  • In a way that is needed/required/is unavoidable

why

Copy vocabulary

US / waɪ /

UK / hwaɪ, waɪ /

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

definitely

Copy vocabulary

US / ˈdefɪnətli /

UK / ˈdefɪnətli /

A2
  • adverb
  • Without question; beyond doubt

sound

Copy vocabulary

US / saʊnd /

UK / saʊnd /

A1
  • adjecitve
  • Sensible, dependable and reliable
  • Unbroken or undisturbed, as of sleep
  • Firm or solid in structure
  • Sane; not mentally ill
  • Clearly reasoned; involving sense, good judgment
  • noun
  • Unique quality that characterizes a style of music
  • Waves traveling in air or water that can be heard
  • verb
  • To seem or appear to be, from what was said
  • To say in a clear deliberate manner
  • To make a noise, e.g. to ring a bell

well

Copy vocabulary

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

statement

Copy vocabulary

US / ˈsteɪtmənt /

UK / ˈstetmənt /

A2
  • noun
  • Record of activity in a bank account over time
  • Act or process of saying something formally

follow

Copy vocabulary

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

less

Copy vocabulary

US / les /

UK / lɛs /

A1
  • adjecitve
  • Smaller in amount or degree
  • adverb
  • To a smaller degree
  • noun
  • A smaller amount
  • preposition
  • With the subtraction of

make

Copy vocabulary

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

than

Copy vocabulary

US / ðən /

UK / ðən /

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

nth

Copy vocabulary

US / enθ /

UK / ɛnθ /

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

term

Copy vocabulary

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

the

Copy vocabulary

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

word

Copy vocabulary

US / wɜ:d /

UK / wɚd /

A1
  • noun
  • Unit of language that has a meaning
  • Promise
  • Short remark or piece of information
  • verb
  • To express something by choosing particular words

this

Copy vocabulary

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

inductive

Copy vocabulary

US / ɪnˈdʌktɪv /

UK / ɪnˈdʌktɪv /

A1
  • adjecitve
  • Arising from inductance

you

Copy vocabulary

US / jʊ /

UK / ju /

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

but

Copy vocabulary

US / bət /

UK / bʌt,bət /

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

fifth

Copy vocabulary

US / fɪfθ /

UK / fɪfθ /

A1
  • noun
  • 5th

would

Copy vocabulary

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

expect

Copy vocabulary

US / ɪk'spekt /

UK / ɪkˈspɛkt /

A1
  • verb
  • To believe something is probably going to happen

dot

Copy vocabulary

US / dɒt /

UK / dɑt /

B1
  • noun
  • Small round mark
  • verb
  • To place small amounts/things in various places
  • To mark something by placing a small, round spot

pattern

Copy vocabulary

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

whether

Copy vocabulary

US / ˈweðə(r) /

UK / ˈhwɛðɚ, ˈwɛð- /

A1
  • conjunction
  • If something will happen or not

not

Copy vocabulary

US / nɒt /

UK / nɑt /

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

reasonable

Copy vocabulary

US / ˈri:znəbl /

UK / ˈrizənəbəl /

A2
  • adjecitve
  • Being somewhat good, but not great
  • Fair and sensible; appropriate

maybe

Copy vocabulary

US / ˈmeɪbi /

UK / ˈmebi /

A1
  • adverb
  • Possibly but not certainly; perhaps

now

Copy vocabulary

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

reasoning

Copy vocabulary

US / ˈri:zənɪŋ /

UK / ˈrizənɪŋ /

A2
  • verb
  • To think and make conclusions in a logical manner

very

Copy vocabulary

US / 'verɪ /

UK / ˈvɛri /

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

they

Copy vocabulary

US / ðeɪ /

UK / ðe /

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

hold

Copy vocabulary

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
  • To agree to keep something for someone
  • To have the capacity to support/contain something
  • To control an area and protect it from attack
  • To not allow someone to leave a place
  • To cause an event to happen at a place or time
  • To use hands or arms to carry or keep something
  • 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

look

Copy vocabulary

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

evidence

Copy vocabulary

US / 'evɪdəns /

UK / ˈɛvɪdəns /

A1
  • noun
  • Factual proof that helps to establish the truth

oppose

Copy vocabulary

US / əˈpəʊz /

UK / əˈpoʊz /

A2
  • verb
  • To fight against someone in a contest or game

all

Copy vocabulary

US / ɔ:l /

UK / ɔl /

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

conjecture

Copy vocabulary

US / kən'dʒektʃə(r) /

UK / kənˈdʒɛktʃɚ /

C1
  • noun
  • Forming an opinion/conclusion with little evidence

fourth

Copy vocabulary

US / fɔ:θ /

UK / fɔ:rθ /

A1
  • noun
  • 4th

yes

Copy vocabulary

US / jes /

UK / jɛs /

A1
  • adverb
  • Way to say you agree or will do something

each

Copy vocabulary

US / i:tʃ /

UK / itʃ /

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

yeah

Copy vocabulary

US / jeə /

UK / ˈjɛə, ˈjæə, jɛ- /

A1
  • exclamation
  • Another way of saying 'yes'

about

Copy vocabulary

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

Copy vocabulary

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

what

Copy vocabulary

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

Copy vocabulary

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’

she

Copy vocabulary

US / ʃɪ /

UK / ʃi /

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

right

Copy vocabulary

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

case

Copy vocabulary

US / keɪs /

UK / kes /

A1
  • noun
  • Container used to carry things, e.g. clothes
  • Set of facts about a crime
  • Set of facts about an event
  • Example or instance of something
  • verb
  • To find out about a place, as in planning to steal

mean

Copy vocabulary

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

number

Copy vocabulary

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

square

Copy vocabulary

US / skweə(r) /

UK / skwɛr /

A2
  • adjecitve
  • Being fair or honest
  • Multiply a number by itself e.g. 2x2 or 6x6
  • noun
  • Shape with 4 equal length sides and 4 equal angles
  • The result of multiplying Length by the width
  • Open public area in the middle of the town
  • verb
  • To make something balance or be equal
  • To multiply a number by itself, e.g. 2x2 or 6x8
  • To straighten the edge to form a four-sided shape

fancy

Copy vocabulary

US / 'fænsɪ /

UK / ˈfænsi /

A2
  • adjecitve
  • Unusual and attractive in design
  • verb
  • To want to have or do something; feel like
  • To imagine or suppose that something will happen
  • To believe or imagine something that is not true

sequence

Copy vocabulary

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
  • Subtitles section
  • Jill looked at the following sequence.
  • 0, 3, 8, 15, 24, 35.
  • And it just keeps going, I guess, with a dot, dot, dot.
  • She saw that the numbers were each 1 less than a square number.
  • 0 is 1 less than 1, which is a square number.
  • 3 is 1 less than 4.
  • 8 is 1 less than 9.
  • 15 is 1 less than 16.
  • Yeah, they were all 1 less than a square number.
  • And conjectured that the nth number would be n squared minus 1.
  • Now conjecture, that sounds like a very fancy word.
  • When someone makes a conjecture, they conjecture, that just means that they're making a statement that seems, or they're making a proposition that seems likely to be true.
  • It seems like a very reasonable thing to say.
  • But it's not definitely true.
  • So she conjectured that the nth number would be n squared minus 1.
  • The reason why this is a conjecture as opposed to a 100% definitely true statement, is we don't know whether this pattern continues.
  • She's just going off of the pattern that she saw so far and she just generalized it.
  • She just assumes that it keeps on going.
  • But we don't know whether it necessarily keeps going.
  • Maybe the next number, you would expect it to be 48, but maybe it's not 48.
  • Maybe it's something weird.
  • Maybe it's 2.
  • Maybe it's 500.
  • And so the conjecture wouldn't hold up if you were to see that, but based on the evidence you see so far it seems completely reasonable that this pattern would continue.
  • And so she conjectured that the nth number would be n squared minus 1.
  • Completely reasonable.
  • Now did Jill use inductive reasoning?
  • Yes, she used inductive reasoning.
  • That's what inductive reasoning is.
  • You see a pattern.
  • In this case, every term in this sequence so far was-- if it's the third term, it was 3 squared minus 1.
  • The fourth term is 4 squared minus 1.
  • The fifth term is 5 squared minus 1.
  • So she saw the pattern and she just generalized it to say, well, I think or I've conjectured that the nth number will be n squared minus 1.
  • That's what inductive reasoning is all about.
  • You're not always going to be 100%, or you definitely won't be 100% sure that you're right, that the nth number will be n squared minus 1.
  • But based on the pattern you've seen so far, it's a completely reasonable thing to-- I guess you could say-- to induce.