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

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

1+1=22×1=22-1=11-1=1duh