Find the sum of the first 9 terms of the sequence. Show all work for full credit.

2, - 7, - 16, - 25,.

-7-2=-9, - 16--7=-9 so there is a common difference, - 9, so we know that this is an arithmetic sequence.

The sum of an arithmetic sequence is just the average of the first and last terms time the number of terms ...

a (n) = a+d (n-1), in this case a (9) = 2-9 (8) = - 70

So the sum is (2-70) (9/2) = - 306