Find the sum of the first 90 terms of the sequence - 4, - 1, 2, 5, 8, ...

Im pretty sure its 11655

This is an arithmetic sequence because there is a common difference of 3, each term is 3 greater than the previous term.

The sum of any arithmetic sequence is the average of the first and last terms times the number of terms ... mathematically this winds up as:

s (n) = (2an+dn^2-dn) / 2, a=initial term, n=number of terms, d=common difference

In this case:

s (n) = (-8n+3n^2-3n) / 2

s (n) = (3n^2-11n) / 2 so

s (90) = (3*8100-11*90) / 2

s (90) = 11655