Question

find the nth term
1 2 3 4 5 6
2 30 88 176 294 ?

Answer 1

http://www.mathsisfun.com/algebra/sequences-finding-rule.html


Terms : 2 30 88 176 294
Diffs : 28 58 88 118
2nd Diffs : 30 30 30



With second differences you multiply by "n^2 / 2" (in our case 30*n^2/2 = 15*n^2):


Terms : 2 30 88 176 294
15n^2 : 15 60 135 240 375
wrong by : -13 -30 -47 -64 -81

We're drifting by -17
So, let's check 15n^2-17n compared to the original terms


Terms : 2 30 88 176 294
15n^2-17n : -2 26 84 172 290
Wrong by : 4 4 4 4 4

We are wrong by 4, so our final answer is:

15n^2-17n+4