# How do I find a formula for s_n for the sequence -2, 1, 6, 13, 22,...?

Jan 28, 2015

I would suggest you to find the formula for ${a}_{n}$ first.

The idea is that the differences have been increasing by 2.
-2 to 1 is +3
1 to 6 is +5
6 to 13 is +7

So ${a}_{n}$ should be quadratic.

One can guess that ${a}_{n} = {n}^{2} + 2 n - 2$

For ${S}_{n}$ it's just the sum from ${a}_{0}$ to ${a}_{n}$

Good luck!