What is the sum of a 7-term geometric series if the first term is −11, the last term is −171,875, and the common ratio is −5?

−143231

The general term of a geometric series can be described by the formula:

an=arn−1

where the initial term is a and common ratio r.

Then we find:

So dividing both ends by (1−r) we find:

N∑n=1an=a(1−rN)1−r

In our example, N=7, a=−11 and r=−5

So: