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

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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!
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[@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.

[@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....

[@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

[@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

[@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

[@hazielllanes973]

So in conclusion u have confused me more

[@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. 😊✌👍

[@ericawu8779]

"arithmetic" who else pronounces it differently?

[@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 😂

[@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.

[@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

[@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

[@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

[@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.

[@shanalaus]

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

[@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.

[@muhammed-amiinmuhamud5387]

im freaking out

[@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 😅

[@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

[@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???

[@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.

[@abdallahraafat432]

PLEASE USE A SLIGHTLY BRIGHTER COLOR THAN SOLID BLACK!

[@zx6r502]

I already know this why am I watching this

[@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

[@bobademon9332]

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

[@madilynharris5969]

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

[@쟈기-k5e]

수학 ㅈㄴ 싫어

[@KingCadmos]

I can.

[@asselann9870]

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

[@pokaay3163]

anyone else studying before their finals say I

[@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.

[@wardielaw7856]

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

[@krutomjer]

Congrats, your accomplishment will be eternally celebrated

[@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

[@bhavinilakshmanan2377]

I HATE MATHS !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1

[@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.

[@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😭

[@katzbeanz]

this helped, me with my math homework,

[@ojk3863]

lol stop using such complicated words xD

[@pokaay3163]

brain cell count 1

[@dognibbler]

imagine having all your subs being teachers

[@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.

[@aki-kf4bo]

Woah this taught me so much

[@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!

[@ProGamer1115]

You completely lost me at 1:07

[@vaishnavchandra5220]

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

[@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.

[@Joci555]

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

[@uncle_.]

Lmao that's all of sal's videos

[@karenoncrack4599]

I get it that you spot and identify the sequence. but who tf needed to write a formula for that? people are strange, just say that each number is x larger then the previous.

[@tr4629]

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

[@Jaiveer101]

आ यो टा नंबर्स 👻👻👻👻👻👻👻👻👻💩💩💩💩💩💩💩💩💩💩💩💩 आर्थमेटिक्स सीक्वेंसेज

[@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.

[@shaqiloneal2605]

what indicates K and d(n-1)

[@lovelydovey7778]

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

[@Spat1o]

funny how im 6th grade and my teacher teaches us this

[@annelissesantacruz9884]

IM SO BAD AT MATH THAT I CANT EAVEN UNDESTAND THIS🙄🙄🤢

[@redheadshield9627]

Yeah because its Math

[@abdalrahmanamrmostafa1975]

ya umm I got 119 = 11,480,... in class so I came here

[@CxffeeBean]

The video just started and I already got distracted by the comments

[@Kcgramerrr]

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

[@78anurag]

Me too

[@bobfredjeojrsrthe3rd490]

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

[@sebperkins5412]

Speaks way too fast

[@supermarikfan]

I'm sorry this still doesn't make any sense

[@usuaan]

lol I have a test on this today wish me luck

[@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.

[@omegasteve8485]

…. I did not understand a single thing you said goodbye im going to the organic chemistry tutor

[@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,...?

[@dbzfan655]

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

[@jaydenchesslife]

Intresting! Great video Sal!

[@cindycharestugaycutie2848]

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

[@abbyadamo2155]

Emma do your work and stop scrolling through the comments

[@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?

[@rskenny4446]

Thanks I need to pass my test

[@honeyandlavender_]

Why do I need this for Psychology, again?

[@hypervenom5960]

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

[@saadabilmona4389]

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

[@elkhouryeliza9715]

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

[@instertname4893]

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

[@myronmteul7613]

Omg thank u so much it really helped allot 😭

[@chanakyaneeti8016]

Nice video

[@anirudhmenon5281]

thank you Mr.Khan

[@shadychannel2782]

im worriying when my teacher say we have quiz next week. i hate math..

[@ayshaabdullah8756]

How was your quiz I have one tomorrow :(((((

[@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?

[@ryanfrizzell736]

Arithmetic sequences = hallmark of life

[@downtownpets]

Are you familiar with who the videos are for?

[@maxsotelo1089]

Very helpful :D

[@seongsik]

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

[@julijoba9002]

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

[@tMalfunction]

he put the dot on the " t ", and not the " i " D: ALL CREDIBILITY LOST

[@yuphengvang3895]

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

[@T_man2143]

*you’re

[@artexanimo5657]

I'm ... Stupid

[@kevh.2652]

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

[@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 🙂

[@lookawayorneverlookagain]

please help guys i have exam in 7 hours is 2,8,32,128... a arithmetic sequences

[@78anurag]

No I'm probably too late but you can write it as: an= 4(an-1) n1=2 for n≥2

[@lookawayorneverlookagain]

@@78anurag thx.. You where a little late tho ( 7 whole months)

[@78anurag]

@@lookawayorneverlookagain I know lol

[@78anurag]

@@lookawayorneverlookagain Uh.... Sorry I checked it it's not an arithmetic sequence but the equation is still correct

[@stuffguy7796]

Mans handwriting bout to make me act up

[@jamahldavis4296]

POV your here bc your teacher can’t explain anything to save her life 🙋🏿‍♂️

[@garretta5804]

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

[@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?

[@TheVincentVanGogh]

Look where this Quarantine led me too..

[@Aristothink]

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

[@dahelmang]

Recursive what huh?

[@dahelmang]

And you've done it and I still don't understand what it is....

[@siennacoventry33]

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