Finding the nth term of a Quadratic Sequence - GCSE Higher Maths

A video explaining how to find the nth term of a quadratic sequence. This topic is on the GCSE Maths Higher course and not foundation. If you want to check linear sequences use this video: • Sequences and Finding ...
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0:00 Intro
0:18 Finding the second difference
1:26 Finding the coefficient of n squared
1:58 Finding the linear part
3:23 Finding the nth term of the quadratic sequence
3:48 A second example
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[@Ramimhasan-rd8oc]

this is the most clear explanation i have ever watched.. Thanks a lot

[@1stClassMaths]

Glad to hear that!

[@RobloxianX]

Thank you so much, my school did a 1 hour lesson on this and they werent able to teach anyone. I sent this to everyone in my class, we are saved! Thank you so much, you're doing gods work

[@Stratmaster_]

You have no idea how much this video helps before an exam!!! 😂 🫡

[@Goose_G.O.D]

😂😂 facts

[@JakeOfShire]

Wow! this was honestly life changing. It makes a thousand times more sense. I no longer look at this question with dread! Thank you 😅

[@pluto_2682]

You just saved me 😭 literally writing my math exam tomorrow .. great video

[@Storm_Fly]

By far the most clear explanation and straight to the point . Thank u sir !

[@staroffixial8159]

Thank you so much! Now im prepared for my gcses :)

[@danielippolito-fletcherscr3273]

This is a spectacular explanation. I am a middle school math teacher who has been struggling to grasp an easy way to explain this for weeks. Thanks so much!

[@1stClassMaths]

Excellent I am glad it was so useful! I picked it up off another teacher a few years ago :)

[@GamingWithJas-ff4yf]

You taught this much better than my teacher, my teacher explained it differently, i did understand but your explanation is way better, thank you a lot im using you to revise for my end of year 9 assessment

[@Lafentity]

Bro thanks so much. This deserves a sub, you teach a much clearer explanation than my tutor.

[@new-qo8rb]

I get so confused -- how do i remember all this? i simply will forget 😔😔

[@z.a075]

this is honestly so so helpful. may god bless you. you have just saved me

[@1stClassMaths]

You're so welcome!

[@truthwins5804]

It helped a lot . Thanks ❤❤❤ I didn’t understand a thing about how to find the nth term of a quadratic sequence but after this video , you would think I was Einstein!! 😂😂 Thanks again😊😊

[@1stClassMaths]

You are welcome….Einstein. 😁

[@theokongnaphakdee9391]

thank you so much!!!! that was very helpful!!!!!!🙏🙏🙏🙏🙏

[@gracehathaway2715]

Honestly, ty so much .I tried to watch the corbet maths video on this and was on the verge of tears 😂.this vid makes so much sense now ❤

[@1stClassMaths]

You're very welcome!

[@tatertotsassemble]

this was so clear! my teacher has been so difficult with explaining it to me lately, and always got annoyed when i asked “too many questions” so i haven’t been able to understand ANY of it. but this cleared pretty much everything up. as a student in year 9, i feel much more prepared for my gcse prep now

[@ieatmentoss1714]

you should get another teacher if they're saying you ask “too many questions”

[@RedditsFunTales]

@@ieatmentoss1714 exactly, school is a place for development. teachers should be pleased if a student asks a lot of questions as it shows their interest in the topic and forecasts they need help. must be a crappy teacher if that is their excuse.

[@PKisBetter]

bro ur doing this in 9th grade?

[@kanan597]

youre in y9 theres no need to be prepping for gcses rn, take it from a y11 :)

[@aleynak-wn5xq]

@@kanan597they still have mocks and internal exams

[@yoitsfaizy8778]

very comprehensible, cheers m8

[@Fire.edits.14]

thank you so much, i tried watching a lot of videos, this is the best and most clear one :)

[@1stClassMaths]

Glad to hear that!

[@alisa6170]

the explanation and visuals were so easy to understand!! thank you so much

[@1stClassMaths]

You're very welcome!

[@user-fg2cn7si6u]

Thank u for the nice explanation. I finally undertood this!!

[@1stClassMaths]

You are welcome!

[@user-hs1pt7ud7r]

Hello teacher so thank you because your teaching so simply God willing every time get happy ❤

[@user-wn5yi3pc5s]

Amazing explanation!

[@Crukks1973]

how do you get the values 1,4,9,16, and 25 as the square numbers

[@1stClassMaths]

1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 4 x 4 = 16 5 x 5 = 25

[@ElaineWilkins-v1k]

You are a legend thank you for explaining it so well

[@1stClassMaths]

Glad it helped!

[@thesingingchef29]

Thank you so much! Also here's another method: a: second diff / 2 b: 3a+b = first diff of first term c: a+b+c = first term Now, all you have to do is sub a, b, and c into the equation T(n) = an²+bn+c. *Leave T and n as variables

[@Bollywoodwiddeepak]

I was trying to find the Nth term of quadratic equation from last two days but could not understand. But you explained it very well in short method 👍

[@MuhammadHammad-k7i]

best explination ever sir thanks a lot

[@user-cm7gf2yh3n]

sometimes theres a sub question after you find the nth term of the sequence where it asks you to prove if a number is apart of the nth term of the sequence that you just found out. how do you do those sort of questions? (also thanks for explaining this topic so well it makes alot more sense now)

[@disappointedshrek8681]

(second difference/2)×n² square numbers multiplied by 2 (including 1) subtract the original sequence by the square numbers multiplied by 2 find the general rule for the new linear sequence brought forth by subtracting the two (first difference×n + first term-x=first difference)

[@mugdha4128]

Man thank you so much for this video you are a legend i have a assessment on this topic and it is worth half my grade aand i didnt understand a thing my teacher taught me vut after watching this video i understand so much that i might just ace the assignment thx so much

[@1stClassMaths]

Fantastic!

[@faizaax4376]

omg i went on like 50 websites trying to get help but this video saved mee

[@1stClassMaths]

50, that’s a lot!

[@tushiglutbekh5453]

you made the problem easy to solve😁😁

[@deonxholi9800]

why is it 4n -1 but not for ex 4n+1

[@hamzasherasmat6593]

sorry to ask, but how did you find a sequence for 3n^2 on the first one, do i just square root like the first one i have to square root, then the second one, then the third one?

[@1stClassMaths]

Don't apologise! For the 3n^2 sequence you do the square numbers so 1,4,9,16,25 then multiply them all by 3.

[@hamzasherasmat6593]

@@1stClassMaths Ohhhh, thanks sir!

[@spxcegalaxy555]

Thank you so much I now understand and tomorrow I have exam you deserve a sub

[@1stClassMaths]

Thanks for the sub and good luck!

[@user-es1pk4og1z]

Thank you very much!

[@charles-np1rc]

thank you helped a lot

[@jacobhaile383]

On the second sequence where did you get the square numbers from

[@1stClassMaths]

Square numbers are from 1x1, 2x2, 3x3 etc

[@rizwanafzal7076]

Very good.thanks for such good video. Very useful.

[@1stClassMaths]

You are most welcome

[@user-dm4sx6kt8k]

Thanks!

[@hutt1232]

Hello, why doesn’t the quadratic sequence formula work here? I do an^2 + bn + c but i get incorrect answers while in other questions i use the formula and its correct

[@1stClassMaths]

Hi. I am not unsure what you mean? Can you give an example and I will try see what's happening :)

[@bangchanstoez]

This helped so much thank you sooook much❤️❤️❤️❤️❤️

[@1stClassMaths]

No problem 😊

[@basselmohamed5680]

The last example is 2nsqure+-3n+5 not 2nsqure-3n+5 ,you forget to put the plus, if you want to work out the first term of the original sequence by using 2nsqure-3n+5 it will be 2-2 which is 0 but if use 2nsqure+-3n+5 it will be 2+2 which 4, in all cases we adding because the third sequence plus the second sequence equal the first sequence

[@1stClassMaths]

Hi. Unfortunately you are not correct here. 2n^2 + - 3n + 5 is equivalent to 2n^2 - 3n + 5 (which is the answer). When you add a negative it is just the same as subtracting. Your errors comes in your substitution. If you substitute in n = 1 you get 2*(1)^2 - 3(1) + 5 = 2 - 3 + 5 = 4

[@gracehathaway2715]

Get told😂

[@toneless4345]

@@1stClassMaths why minus first, what about bedmas, 2-3+5, don't u have to add 3+5 first, which would give u 8?

[@supariley]

THANK YOU SO MUCH

[@1stClassMaths]

NO PROBLEM

[@usmanayoub1434]

Thank you it's working

[@olusola9757]

Thank you so much 😀

[@zafarziya-ip3dq]

Thank you so much ❤

[@1stClassMaths]

You're welcome 😊

[@andrewr3243]

What happens if 2nd difference is an odd number like 5? Would nth term be written starting with 2.5n

[@1stClassMaths]

Yes

[@andrewr3243]

@1stClassMaths wow thanks for the super swift reply!! 😁😁

[@pen7822]

god bless you wonderful man

[@1stClassMaths]

Thanks!

[@basselmohamed5680]

Your video is very helpful

[@1stClassMaths]

Glad you think so!

[@Pegasus10707]

thank you 😊

[@1stClassMaths]

You're welcome 😊

[@seblemekete8413]

Thank you so mach😅 you save ME if i donot see this vidio i will get

[@arqhur]

thank you!

[@xmayx2507]

THANK YOU

[@user-og6vl2ms2s]

thank you very much bro.............

[@1stClassMaths]

Thank you too :)

[@remarkablething5874]

cheers mate

[@ratchet7748]

Thanks so much!

[@1stClassMaths]

You're welcome!

[@wewiee]

What if the second difference is not constant?

[@1stClassMaths]

The sequence is not a quadratic sequence.

[@shayanghasemi1993]

Thanks a lot

[@1stClassMaths]

No worries!

[@educationservices7426]

Why we use the 1,4,9,16,25 values to multiply with woth to get the answer 3,12,27,48,75...kindly anyone plz help me at this stage bcz I didn't get the point from where we get 1,4,9,16,25 values

[@1stClassMaths]

They are the square numbers.

[@educationservices7426]

@@1stClassMaths ...and in the last how he get -1 that is the value of c he find out ..how it comes?

[@shahdahmed6436]

THANKYOUTHANKYOUTHANKYOUTHANKYOU!!!

[@1stClassMaths]

NP

[@samaaa8400]

THANK U SM

[@1stClassMaths]

No problem

[@user-so5qr5jh8p]

What if the answer after subtracting the sequence is a sequence that has the same number

[@1stClassMaths]

Great question. This just means the nth term of it is simply the constant number. So if it's always 3, 3, 3, 3, your nth term might be something like n^2 + 3

[@user-so5qr5jh8p]

@@1stClassMaths ohhh thank you so much❤

[@NpcFR01]

What about having 3 layer on the sequence?

[@1stClassMaths]

It would be a cubic sequence

[@NpcFR01]

@@1stClassMaths is that any method to solve it?Btw thank you for your response

[@1stClassMaths]

Hi yes there is but it is not needed for GCSE. Search for cubic nth term videos. 😀

[@MarieAddo-Tetteh]

Thank you😊

[@1stClassMaths]

You're welcome 😊

[@zeemish]

thanks!

[@1stClassMaths]

No problem!

[@wandaxmayfield14]

I dont grt why u added 5 on the 2nd equation

[@s4-yt]

10 mins before my exam 😂

[@RoBotOnd]

5:16 how did u get the +5!? Pls 😢answer brother i got an exam tomorrow

[@1stClassMaths]

To get from -3 to +2 (the first term) we add 5

[@RoBotOnd]

@@1stClassMaths Thank you so much!! ❤️

[@KOZBON-lv8zy]

i did this question and I got 2nsquared - 1n + 3, can you tell me what i did wrong? - (2,7,16,29,46)

[@1stClassMaths]

It is 2n^2 - n + 1

[@KOZBON-lv8zy]

@@1stClassMaths Oh really? Chat gpt is wrong then 🤣 THANK YOU!!!

[@1stClassMaths]

chatgpt is pretty bad at maths.

[@omarbouhassoun1775]

In the second example it’s supposed to be 3n-1 not 3n+5

[@1stClassMaths]

Well it is actually neither of those. It is -3n + 5 since -3 + 5 = 2

[@charcoalotte2021]

Okay so the thing is my sequence is 4,9,16,25 how do i do that?

[@1stClassMaths]

Same way. The second difference is 2 so you have n^2. Subtract this (1,4,9,16,25) from the sequence and you get 3,5,7,9,11 The nth term of the linear part is 2n+1 so n^2 + 2n + 1

[@alescuzyehhh]

@@1stClassMathsoh wow you replied to soo many comments!! that mustve taken a long time ahah.. thank you so much for this video, its so helpful.. i was struggling to understand it in my class but this made it so much easier for me!!

[@1stClassMaths]

I try to answer as many of the questions as I can.

[@alescuzyehhh]

@@1stClassMaths 😂😂😂

[@Yche-21M]

bro how you did that 2:18 3n²

[@1stClassMaths]

Bro not sure what you mean? Where did the 3n^2 come from or how did I get the numbers 3, 12, 27, 48 and 75?

[@nicole27777]

because you halve the second difference (6)

[@LovelearningAgain]

Thanks a bunch. To the point. If you don't mind, what is the name of the software that you used in this video?

[@1stClassMaths]

Thanks. I use powerpoint.

[@nicolaeveritt5555]

Thanks so much

[@1stClassMaths]

You're welcome!

[@talharafaqat3084]

I didnt get a linear sequence the question was find the nth term of the sequence 4,9,16,25,36

[@wikaarad]

This was genuinely so helpful and clear thank you 🙏🏼

[@1stClassMaths]

You're welcome!

[@falingunit]

you can actually apply the same idea to find out the nth term of any polynomial

[@frigid.editzz]

I DID understand

[@StrikingStew]

saved the paper 2

[@sephorarufai]

thank you broo😭 my teachers can’t explain it properly. but why tf would i need to know how to find an nth term?? it’s so long asw like what the heck

[@k.kai2434]

Ikr idek why but at least i can do it now💀

[@drrkwolf]

a+b+c = first original term 3a + b = 1st diff first term 2a = 2nd diff first term a+b+c = 8, 12, 20, 32, 48 3a+b = 4, 8, 12, 16 2a = 4, 4, 4 a = 2, b = -2 c = 8 2n^2 - 2n + 8

[@L0St_Memories0]

yea i was searching for this

[@Sadisfynotfound]

5:06 i dont understand the linear part because 2(1)^2 is 4 but you said 2!!!!!!!

[@Sadisfynotfound]

ok i understand now thx

[@user-ek7bq8tp7v]

I didn't understand

[@galaxyz3709]

Practice and you will get it

[@alescuzyehhh]

@@galaxyz3709yep!!

[@waleedmalik785]

If you want a easier way to find b,the equation 3a + b=the first term of the first sequence.It will give you value of b,you can find the value of c using the quadratic equation,an2+bn+c,put the value of a and b and find c,btw the 2 in an2 represents the n being squared.

[@pces.x]

I don’t, I don’t get it

[@GamingWithJas-ff4yf]

What its so easy

[@user-rubbishsoup]

even with the best explaination vid about nth term Quadratic Sequence, it still sounds complicated enough. This shows how stupid this tpoic is

[@k.kai2434]

Yeah 💀

[@jamespiggin4612]

Class video

[@1stClassMaths]

1st Class

[@omnath3577]

Anybody can solve this Find the nth term of the sequence 3,5,10,22,47,93

[@abdelrahmanmohamad9190]

I suck at this chapter

[@k.kai2434]

Same💀

[@Twilamation4643]

Not really helping but at least I have an idea on what the nth term of 5 7 11 14 19 is

[@xlldx]

is it just me or does this not help AT ALL😭🙏🏾

[@1stClassMaths]

Maybe just you :(

[@HassanKhan-oc6fp]

Thanks!

[@trabbelsiskyee]

THANK YOU SO MUCH

[@1stClassMaths]

You're welcome!

[@user-dm4sx6kt8k]

Thanks!

[@1stClassMaths]

No problem!