The sum to infinity of a geometric progression is −110 − 1 10 and the first term is −18 − 1 8 . Find the common ratio of the progression.

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.

Answer Details

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