nth term of a quadratic sequence - the easy way - GCSE level 6+

This video is all about finding the nth term of a quadratic sequence and forms part of the playlist on quadratic sequences . I've also added to the playlist on GCSE higher revision.

The question is aimed at around level 6+ GCSE maths:

Find the nth term of 5, 9, 17, 29, 45 sequence of numbers.

I tend to use 2 formulas 3a + b = the difference of the first two numbers, and a + b + c = the first number. Once you've calculated these you should be good to go.

I hope the video helps and please do leave a comment - thanks!

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[nishisharma]

This is the best way to learn, you didn't have to draw any tables or anything, thank god! This was a lifesaver, thank you so much

[stefanc]

I have been waiting for around 1 and a half years to find an understandable method for this and now i have it, one day before my mock gcse maths non calc ...Thanks a lot though much appreiacted Mr Deacon!

[tari-starremichael]

literally watched 7 videos on this and didn't get any of it until this explanation! Thank you so much!

[karolisz]

my exam is tomorrow and only now I learnt this question

[Vxer]

Omg thanks I now finally get it, I’ve been trying to find out how to do nth term of quadratics for ages!

[alexchristiannhudtwalcker]

You have saved my life. Wish you the best!!

[.ridamehakaziz]

Very easy and quick way to solve these . Really happy found this 👍

[tanak]

daaang you are the best i got it in sec evn corbett maths couldnt help

[johnbingham]

Incredible.You could not have made it simpler.Thank you very much.

[nayabfatima]

U r amazing!!! Deserves a noble prize i mean thats how much respect u just gained from me!!!

[amaleshteiwi]

Thank u so much. You r better than my teacher

[Ahsan]

Best video on sequence ever made what a brilliant trick

[benjaminsp]

Thank you so much absolute legend you have saved me

[bibi]

Very good but Please explain more for every step; another words, explain step by step what happens. Thank you. Very helpful

[nickbarkas]

Hello, is it possible to solve it without the 3a+b formula; The minus sign troubles me since the 2n squared results give an arithmetic sequence... How to figure out it is -2n;

[amnabhatti]

You can also do it another way : so basically go one step back from both differences. The 3 numbers you get after can really help get the answer in a similar perhaps easier way:
the bottom number remains like you said 2a then the number above is a + b and then the top one is c then just put it back into the an^2 + bn + c. Done. This method is guaranteed to be corect!
Eg:
3 , 9 , 21 , 39
^ +6 ^+12 ^+18
^+6 ^+6 ^+6 ---- HERE go back one step
so 3 , 3 , 9 , 21 , 39
+0 +6 +12 +18
+6 +6 +6
c = 3
a + b = 0
2a = 6
so now rearrange to get a then b then you know c is 3
so a = 3 and b = -3 and c = 3
So end answer is 3n^2 -3n + 3

[stephenbarker]

the way i learnt was when found 1st term subtract square numbers from the original sequence then find nth term of new sequence and put the experssions for both together

[madster_]

Where did we get the 3 from in 3a+b=4??? Xx thank you this is really helpful

[Rawan-ogij]

Thanks a lot man this really helped, keep up👍🏿

[ghst_-hfol]

Thank You ever so much. You are a lifesaver