How to find a formula for a quadratic sequence (3 examples)

How to find an explicit formula for a quadratic sequence? First, we check the difference of the difference of the sequence. If the 2nd order difference is constant, then we can be sure that the sequence is quadratic with the general form of an=An^2+Bn+C. Then we can use the first 3 terms of the sequence to set up a 3 by 3 system of equations involving A, B, C and then solve. This tutorial is for precalculus students and calculus 2 students. For more future videos, be sure to subscribe: 👉 bit.ly/just_calc
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#calculus #bprpcalculus #apcalculus #tutorial #math
0:00 example 1
5:20 example 2
7:46 example 3

[@emanuelvendramini2045]

Very nice video and I've loved the trick with A! I think that you could use one more trick for the first difference in order to get B, 'cuz the formula for the first difference would be A(2n+1) + B. Taking the last example, once we know that A = 6, taking the first term of the first difference we get 18 = 6(2*(1) + 1) + B = 18 + B, and then B = 0. Finally, C can be obtained with the first term of the sequence, using that A(1)² + B(1) + C = 1, we have 6 + 0 + C = 1 and therefore C = -5.

[@yoav613]

Nice way. I always solved it like i learned in school a2-a1=b1 a3-a2=b2..an-a(n-1)=b(n-1) so summing all we get an=a1 +(b1+b2..+b(n-1)) which is the sum ofn-1 arithemetic series.

[@1224chrisng]

I guess that's like the discrete version of an integral, that's interesting

[@Yaraisme13]

Thank you so much for this!
I have a math hw which is due tomorrow and i didnt understand the lesson that much, but thank you again for your help !

[@petereziagor4604]

Nice and easy 👍
Thank you

[@mathsandsciencechannel]

Great video

[@danpost5651]

You can create a new series by subtracting An^2 from the original series (you only need the first two values in this new series). Then the first difference will be equal to B. Then, subtracting A1 and B1 from the first value in the first sequence gives you C

[@theratingguy5659]

nice video thanks

[@D_folder]

Finally someone who does it properly😢

[@pingudash2420]

hi sir this is very cool

[@pencil6711]

lmao the pokeball

[@jamesstrickland833]

(2nd level diff)/2*(n-1)(n-2)+(1st level diff)(n-1)+a1 ... boom

[@kxraxh]

wala na 'kong magets. kaso pag bumagsak hindi ako makakapagtapos, pag 'di ako nakapagtapos hindi ako magkakatrabaho, pag wala akong trabaho magkakasakit ako, kapag nagkasakit ako mamatay ako kasi nga wala akong pambili ng gamot kasi wala akong trabaho. kaya shet panoodin ko ulit 2hs loop (nahihilo, nalilito)

[@dimi1357]

A shortcut you can use is to generate a_0 (because you can calculate the difference between a_0 and a_1), and then you get C for free because: a_0=A*0^2+B*0+C=C.

[@broytingaravsol]

新開的頻道?

[@Owenwtf]

WRONG THIS GUY IS LYING, IT DOESN"T WORK