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.

$-\frac{1}{5}$

$-\frac{1}{4}$

$-\frac{1}{3}$

$-\frac{1}{2}$

Correct answer is B

S_r = $\frac{a}{1 - r}$

$-\frac{1}{10}$ = $\frac{1}{8} \times \frac{1}{1 - r}$

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

$-\frac{1}{10}$ = $\frac{1}{8 - 8r}$

cross multiply...

-1(8 - 8r) = -10

-8 + 8r = -10

8r = -2

r = -1/4

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