Quadratic/sequence

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I have no idea how to work out the values of a and b. Using the constants (0, -1, -4, -10, -20, -35), I was able to work out that you get a constant difference of -1 but don't know how to get to aw^3 + bw. Please explain how to work this out (question and mark scheme answer are attached below).

https://ibb.co/wrWspcz

https://ibb.co/NVJzC6N


Past paper: https://ibb.co/vwF1Yd0
Mark scheme: https://ibb.co/hyPZntR

Its probably easiest to write it as two simultaneous equations. So picking the first two rows (smallest w) then
0 = a*1^3 + b*1 = a + b
-1 = a*2^3 + b*2 = 8a + 2b
Solving simultaneously gives the values in the ms

Thanks a lot for this.

I also just found this - https://www.youtube.com/watch?v=ckH7MaF_a8Y&t=159s. It shows how you work out the Nth term of a cubic sequence (for anyone else interested in knowing). Although, personally I don't recommend using the method shown in the video, it is just nice to know how it is done : )

Agreed. Here theyve told you that you only have two (non-zero) terms in the cubic, so solving as a couple of simultaneous equations is probably easiest, especially as the first one is
a = -b