Introduction to arithmetic sequences | Sequences, series and induction | Precalculus | Khan Academy

Practice this lesson yourself on KhanAcademy.org right now:
www.khanacadem...
Watch the next lesson: www.khanacadem...
Missed the previous lesson?
www.khanacadem...
Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Precalculus channel:
/ channel
Subscribe to Khan Academy: www.youtube.co...

[@farvamo]

U explained me how to do it in 1 minute and my math teacher had 50 minutes and didn't teach me crap. THANK YOU

[@dakotahippo9]

OH MY GOD!!!! SAME

[@CrisMadla]

Same teachers need to learn to teach lol

[@farvamo]

Or atleast use these videos in class

[@isaaca7372]

agreed

[@upendersingh9980]

l p I am sorry....

[@user-hl6zs5jd4b]

*pretends to understand*

[@B1SQ1T]

*actually understands*

[@unexplained1396]

I have never related to something so much in my life

[@ann1ka_p]

U know what they say 😂 fake it till ya make it

[@trunchwood5908]

Am blank like seriously 😑

[@jetski2322]

Dudeee sameee. I’m dumb.

[@mayarae6272]

You are literally my math teacher. THANK YOU. In my math class we got 2 days to learn this AND piecewise functions, not to mention the fact that our paid teacher has no clue what she's doing. Honestly, thank you, you're the only reason I'm not failing at this point.

[@Anonland]

This is a useful math skill necessary in everyday life.

[@pokaay3163]

funni jok

[@graceykb6392]

Ok boomer

[@trevorking7461]

R/woooosh

[@JoJo-sb8gr]

Cap

[@tempdraw5428]

Never knew 🤣ok suree I thought this was olny used when your a mechanic but yes this was very helpful. 😊✌👍

[@chillwatermelon7780]

My math teacher said if I didn't know this after him writing it out then I was challenged. You just explained it and I understand. Who's big brain now?

[@ShoddySheep.]

ur the goat

[@Matthew-McCallister]

Currently trying to teach myself Calculus II as my campus has shut down for the remainder of the semester and classes are online. I am a math major so now I have to teach myself calc based physics, Statistics, and Calculus all at the same time from home. This helped so much. Thank you!

[@Heyoo1400]

My kid is studying this in grade 9😂😂

[@princelazaro4943]

and your point is? your kid is getting introduced to arithmetic progression, series is a lot more, it leads to the discovery of calculus and limits@@Heyoo1400

[@Heyoo1400]

@@princelazaro4943 bruh why r u taking this so seriously 😂😂

[@ravikiran4495]

@@Heyoo1400 cus you're just that dense Sorry to say

[@haniyaya]

@@Heyoo1400 haha im in 9th grade and currently learning this too 😅

[@cheezytm478]

Me: hey, what’s the speed limit? I can’t see from here. Friend: oh yeah, it’s an=a1-d(n-1)

[@sopiayeoja2823]

Can we really do that?

[@patrickdavezapanta5644]

I read this as anal

[@tdch1767]

It's an=a1+(n-1)d I guess

[@latanyachikamhi3111]

confused asf

[@onelson138]

I HATE ALGEBRA WITH A BURNING PASSION

[@bhavinilakshmanan2377]

same here

[@user-gi2od4zg9q]

I hate Geo with the same kinda passion. Sigh.

[@kev1257ful]

MASTER NELSON living off borrowed time the clock ticks faster

[@commanderxx2617]

Nah algebra is lit fam

[@views-dz7cg]

I hate algebra almost as much as I love MF Doom

[@antonnchindo6006]

I never listen in the math class KZbin math tutorials explain my work in 10 min ain't got time for 2 hour lectures

[@oliviadandreabrooks4658]

yes! preach! i tell all the younger students in my school to just youtube it

[@johnpaulodulay4813]

***** math antics

[@guynumber20]

youre just a lazy teacher we only come on here because of "teachers" like you

[@abdalrahmanamrmostafa1975]

Anton Nchindo my teacher woke me up by spilling water on me 😂

[@bloodykills7509]

*QUIT READING THE COMMENTS AND GO BACK TO STUDYING.*

[@zerglingist]

Shush your mouth you flashback inducing maniac.

[@Queen.jeanae]

Okay okay I’m sorry

[@abbyadamo2155]

leave me alone

[@rachel3.o789]

I feel attacked but thank you

[@aki-kf4bo]

No

[@tripppurviance2083]

Where do I donate? My 14 year old and his mother were at their wits' end last night trying to figure this out in a common core math book. Watched this 7 minute video, did homework, went to bed. THANK YOU!!!!

[@pigeonlove]

Wow you have Google to find the video and you don't have Google to find out how to donate...

[@views-dz7cg]

@@pigeonlove Google is a multi-billion dollar corporation that profits off selling the data of all of their users for advertisements. How much money have they already made off of you?

[@fushiie9583]

@@views-dz7cg and yet here you are...commenting on a google account.

[@ericawu8779]

@@pigeonlove maybe she does know how to donate, she's just sayin' she gonna donate cuz this hella useful Edit: and sometimes google's doesn't find you everything Edit: oh ya, lastly, she might've gotten this from khan academy or youtube NOT google lmao

[@boniquer931]

lucky ur 21 now and u finished from school

[@hazielllanes973]

So in conclusion u have confused me more

[@aileen_0714]

That made so much sense, my teacher took like a week to explain you took just 4 minutes of explanation and now I get it THANK you I have a test on this today I had to see it😭

[@simon333_]

Its almost 4am and I have my precalc exam tomorrow...

[@anthonyespiricueta7493]

And now I'm in your shoes💀😭😭😭

[@chris-gd6tu]

Mood

[@kittenkitchen9641]

Kvyla S omfg same

[@willsimpsart]

Same but I have it in an hour

[@ohgodyourefat4787]

kayla it’s been 2 years but how did you do

[@edwinniemandt1995]

WOW THIS IS GOING TO HELP ME IN THE EVERYDAY WORLD. 👍👌

[@thecornseller]

nice one bro

[@nakamurasupermario64miyamo61]

I thought exactly like this in high school, now I have an anime profile picture and I'm making $13 an hour at a dead end job trying to re-learn math to go back to school.

[@Whatyulookinat]

@@nakamurasupermario64miyamo61 hi… what happened ? U returned to school?

[@nakamurasupermario64miyamo61]

@@Whatyulookinat I recently got a raise to $25/hr at the same "dead end job" I was referring to. Getting good at math was a big part of that though because it kept my mind sharp and able to sort out complicated situations in a very efficient way. I'm still studying math because it's difficult and not having a mountain to climb is boring and depressing.

[@nayshaprasad8318]

depends on the job you take???

[@Miss_Yuriko]

dude. ty so much. I couldn't comprehend anything during class today and I suddenly feel like an arithmetic sequence god now that Khan academy explained it.

[@chadedgeworth9369]

What would we do without Kahn Academy

[@shatter3374]

@Alan Guchemand facts like when am i gonna use this!?!?!?! in life

[@anon8197]

@@shatter3374 pretty sure society wouldn’t be as advanced as it is if students weren’t forced to learn this, but who knows.

[@asselann9870]

You can also write d= a2-a1 , to find the common difference. 💖

[@katzbeanz]

this helped, me with my math homework,

[@reptilelover2129]

Different math types are specific to each job. So to the people who are asking "WHEN AM I GONNA USE THIS!?!?" It honestly depends where you work.

[@nakamurasupermario64miyamo61]

I said the same thing during my math classes in high school and looking back, that's probably one of the worst mindsets I ever had. I graduated not knowing what I really wanted to do. Now I'm 23 and want to be an engineer and I have to relearn everything if I wanna go back to school.

[@nakamurasupermario64miyamo61]

@Lil smackaroo Yeah, go for it and aim high. After high school it's easy to hop into an entry level job "temporarily" and before you even have time to realize it, you're 23 and watching everyone you went to high school with graduating college and getting their dream jobs. Fortunately that slapped me in the face while I'm still young and have at least 42 years of career left.

[@digo901]

Thanks from Brazil. You're helping with math and with my listening in English! :D

[@lucasants4872]

I too XD. I am 13 years old and I have been only watching videos in english and reading english books in PDF to practice my english.

[@user-fh2rw9zh8g]

​@@lucasants4872hello there, you're now 16 years old. I hope you keep up this mindset

[@krutomjer]

Congrats, your accomplishment will be eternally celebrated

[@dbzfan655]

I remember this in High School. It was pretty straightforward. Thank you for the video.

[@vaishnavchandra5220]

Thank you so much. U hv'e no idea how many lives u have saved

[@wardielaw7856]

Literally understood this in like 30 seconds after you explained it but my math teacher couldn’t in a 70 minute lesson

[@aki-kf4bo]

Woah this taught me so much

[@mrdxb1154]

Easier way : check how many it adds up every time then turn it from positive to negative or negative to positive then the first term minus the change negatively for example -5 -3 -1 5n-7

[@melvinramos2849]

MrDXB wait what? I’m confused

[@shak273]

Me who still doesn’t understand:

[@lessthanpinochet]

The way he explained it was just fine and will resonate with more people.

[@charmingcurls7401]

When my teacher is explaining this in school, i don't understand a thing. But somehow this guy on the internet explains it in 7 minutes! Thank you so much!

[@muhammed-amiinmuhamud5387]

im freaking out

[@tr4629]

this saved me when i wasn't getting the difference between the concepts at all

[@shanalaus]

When you want to learn then your internet suddenly turns off: *i just lost my motivation to study*

[@saadabilmona4389]

Arithmetic sequences can be a set of succeeding numbers that are decreasing. The common difference can be a negative number

[@Aristothink]

Arithmetic Sequences are amazing. It's a good exercise to massage to reinforce math in our brains. Great video. Khan is wonderful to help our students 🙂

[@lovelydovey7778]

Thank you for this video I understand it now thanks again!

[@bobfredjeojrsrthe3rd490]

Thx man you helped me more in the first 2 minutes than my teacher did in 50

[@jijgmfamily3210]

this is so confusing wtf is n

[@kingviper5700]

the index

[@TortureBot]

I thought I understood number sequences, and then I watched this video.

[@hazielllanes973]

Kingviper what’s that

[@kingviper5700]

@@hazielllanes973 it depends really, it can be the power (how many times you multiply), or an arithmetic progression (continuous increase of values where the difference is constant) and multiply from those numbers. I think, I've forgotten about this video, so it might not be related, what I've just said

[@hazielllanes973]

Kingviper thanks

[@clownsRscary1]

as i watch both rick and morty and the big ban theory i understand all of this,

[@reptilprinceoflizardpeople5797]

Yet you can't spell bang. Bazinga.

[@instertname4893]

Thanks there’s a test about this tomorrow and this helped

[@hypervenom5960]

Well ACT exam in 4 hours and now I’ve can cross this off a long list of rules I need to revise.

[@Aristothink]

I love math sequences and specially Khan Academy. Great video !

[@zx6r502]

I already know this why am I watching this

[@jaydenchesslife]

Intresting! Great video Sal!

[@tedchoi8488]

I know that this is not a arithmetic sequence, but what should I say with the common difference of numbers of range in quadratic such as 1,4,9,16,25,...?

[@yuphengvang3895]

Thank you so much for this video!!! Now I know how to solve this! Your the best

[@T_man2143]

*you’re

[@bobademon9332]

*Sweats and pretends to understand while mom glares at me*

[@carlylexa6113]

I am literally sitting in bed sobbing trying to understand this. please tell me I am not alone I can't take school anymore

[@78anurag]

It'd ez to understand lol

[@madilynharris5969]

When I understand this in 4 mins and my math teacher couldn’t explain it well in a 1hr and 45 min class

[@anirudhmenon5281]

thank you Mr.Khan

[@ryanfrizzell736]

Arithmetic sequences = hallmark of life

[@myronmteul7613]

Omg thank u so much it really helped allot 😭

[@abdallahraafat432]

PLEASE USE A SLIGHTLY BRIGHTER COLOR THAN SOLID BLACK!

[@ericawu8779]

"arithmetic" who else pronounces it differently?

[@wasimgill4101]

Khan Academy, u do wonderful work, but can background of videos become lighter color like white or grey?

[@Joci555]

Idk if this helped me or made me more confused butttt thank you 🙏🏽

[@uncle_.]

Lmao that's all of sal's videos

[@dognibbler]

imagine having all your subs being teachers

[@Kamrul_abc]

You have explained with some kind of notation here. Where the lower limit is n=1 and upper limit is infinity. My question is what is that notation? Where can I know more about it?

[@garretta5804]

Is defining an arithmetic sequence how you answer it? also what does the (n-1) mean? what is its purpose??

[@JohnTeller-y4k]

Thanks for the video

[@cindycharestugaycutie2848]

Good morning, I just want to ask permission to use this video for my class discussion purposes only. Thank you!

[@KingCadmos]

I can.

[@ickyngo1025]

This is helpful !!❤

[@maxsotelo1089]

Very helpful :D

[@shawnjung6799]

TYSM

[@rskenny4446]

Thanks I need to pass my test

[@honeyandlavender_]

Why do I need this for Psychology, again?

[@pixelfish3395]

How did I sit through and hour of my teacher trying to teach this and walking out with less understanding of math than before I walked in, but come here and know how to do math in ten minutes?

[@Tump3039]

Great Video

[@shaqiloneal2605]

what indicates K and d(n-1)

[@ziziphobusakwe1704]

Thank you so much.

[@user-lt8vl4tr8p]

GOD, I HATE MATH!

[@calicowav]

HATE, I GOD MATH

[@xaviersson7047]

I, MATH GOD HATE!

[@manjotpadda]

I,GOD HATE MATH!

[@benyosef6570]

GOD, MATH I HATE

[@allentowncola937]

Palmtop Tiger thats impossible.You just hate the uncomfortable feeling of not being able to understand it.

[@WWJDinAlaska]

I dont know if I'm more confused or not. I'm stressing out, I am failing school. Also told my teacher I would do my homework and I have a meeting with her first thing in the morning. But it's 1:30am and I don't understand still. I'm so bad at math and school. My teachers at school are not good at their jobs either.😨 also why is letters aloud in math.

[@Kcgramerrr]

Is this actually PreCalc? I'm learning this in algebra 1

[@78anurag]

Me too

[@jakelorkin2661]

I watch rick and mortimo as well as bing beng theory, so concepts such as these are simple to my superior mind.

[@user-hl6zs5jd4b]

Jake Lorkin I watch My Little Pony so my intellectual brainpower is far superior than yours.

[@neurosynchron]

I watch Motu Patlu once. My current IQ is 8000.

[@turd6701]

I watched Boku no Pico and I am a living embodiment of an intellectual.

[@augustusprime0_o]

You explained this so well 😭

[@uncle_.]

Cap

[@kevh.2652]

isn't (n-1) supposed to be an exponent to 2 instead of alongside it?

[@TheVincentVanGogh]

Look where this Quarantine led me too..

[@jennabaily2282]

😔guys I need your prayers, I got my eoc tomorrow.

[@lemonlime07]

Jenna Baily how did it go?

[@jennabaily2282]

Suhani Rampuria it went well and I passed.

[@lemonlime07]

Jenna Baily congratulations 😀

[@jennabaily2282]

Suhani Rampuria thanks.

[@elkhouryeliza9715]

How can we determine the next term of an arithmetic sequence? A can someone please answer me I'm so confused...

[@chanakyaneeti8016]

Nice video

[@notteam6560]

I love you thank you

[@julijoba9002]

i have eoc testing in a week, im speedrunning studying when I've never studied...

[@pokaay3163]

anyone else studying before their finals say I

[@angel-hh1wz]

what does the (n-1) mean? _please help me_

[@ryanpowers8973]

*my exact question like where does that 1 even come from AHHHHH*

[@angel-hh1wz]

@@ryanpowers8973 i think i understand it now, the -1 (in n-1) represents the "previous term"

[@ryanpowers8973]

angelxxxc ahh that makes a lot more sense. Thank you!

[@78anurag]

@@angel-hh1wz Yes you got it!

[@princesspeachgaming4162]

i can't wrap my head around why you use n-1

[@nazarm6215]

It's simple. Plugin in 1 and subtract one and you'll get the value for a of 1, to get a of 2 you need to subtract one, otherwise it will give you the 3rd term

[@HeavenlySunset24]

@@nazarm6215 This makes no sense

[@teetsieroll4529]

Nazar Maksymchuk ohhh thank u so much

[@78anurag]

Because the first pattern for example adds the previous number of a number in the set with 2. So a number in that set is equal to the preceding number +2 (Just look at the pattern, it follows that way, the pattern itself means that adding to a number in that set gives you the next number, meaning that (a number in that set)+2= next number. Ultimately leading to that the number which we added 2 to is the predecessor of the next number since the operation of adding by 2 gives us the next number). We are going to assume the position of a number in the set as n. The predecessor of that number will be at position (n-1) (since the predecessor is one position behind) . From my opening sentence we can write a number as the sum of the predecessor and 2 I.e (n-1)+2. (I'm just repeating this again) So we get, For a number z with position in n in the set its value is going to be it's predecessor number+2= An-1 +2 z= An-1 + 2 A is just a notation for any number so we can replace z with A. A= An-1 +2 Where n is the position of place the number is located is in the set. Simple as that.

[@lorrainegibbons2468]

Satisfying 😣✅✅✅🔥🔥

[@seongsik]

yeah, but how did he write it with the n=1 to infinity thing

[@abbyadamo2155]

Emma do your work and stop scrolling through the comments

[@usuaan]

lol I have a test on this today wish me luck

[@leelorenz.3889]

On the first example why is it two? I mean the gap is only 1 no. right?

[@stuffguy7796]

Mans handwriting bout to make me act up

[@santoshkothekar8558]

Nise sir

[@yaaaserrr]

Thank you :)

[@poopty5150]

6:33

[@siennacoventry33]

Why is it n - 1 on the first questions??

[@ehteshamkhanjadoon9814]

why sequence has positive domain and not negative ? replay as much as possible

[@selahstrain1010]

in the a'n' or a'1' what does the 'n' and '1' mean ?

[@amyhilling3094]

What programme do you use when writing

[@zuesr3277]

Artrage

[@alysaloo341]

explicit recursive

[@SamGOlave]

Me watching this to make a copy of this exact video

[@chris.s6768]

I thought you were supposed to use Un and Usub 1 U sub 2 etc for your nth terms… im confused why are you using k and a, I thought a represents the first term or is this different the american way?