The sum to infinity of a geometric progression is \(-\frac{1}{10}\) and the first term is \(-\frac{1}{8}\). Find the common ratio of the progression.

A.

\(-\frac{1}{5}\)

B.

\(-\frac{1}{4}\)

C.

\(-\frac{1}{3}\)

D.

\(-\frac{1}{2}\)

Correct answer is B

Sr = \(\frac{a}{1 - r}\)

\(-\frac{1}{10}\) = \(\frac{1}{8} \times \frac{1}{1 - r}\)

\(-\frac{1}{10}\) = \(\frac{1}{8(1 - r)}\)

\(-\frac{1}{10}\) = \(\frac{1}{8 - 8r}\)

cross multiply...

-1(8 - 8r) = -10

-8 + 8r = -10

8r = -2

r = -1/4