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

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Answer 1 · 2015-01-28T16:48:37

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+2n-2#

For #S_n# it's just the sum from #a_0# to #a_n#

Good luck!