Question

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?

Answer 1

Answer:

−143231

Explanation:

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:

(1−r)N∑n=1an=N∑n=1arn−1−rN∑n=1arn−1=a+N∑n=2arn−1−N∑n=2arn−1−arN=a(1−rN)

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:

7∑n=1(−11)(−5)n−1=

Answer 2

The answer is -143231 
hope this helps:]