JAMB 2012 · UTME · Q20

The sum to infinity of a geometric progression is $-\frac{1}{10}$ and the first term is $-\frac18$ . Find the common ratio of the progression.

Worked solution (try it first)

Use $S_\infty = \dfrac{a}{1 - r}$ , so $1 - r = \dfrac{a}{S_\infty}$ .
Divide: $\left(-\frac18\right) \div \left(-\frac{1}{10}\right) = \frac{10}{8}$
$= \frac54$ , so $1 - r = \frac54$ .
So $r = 1 - \frac54 = -\frac14$ , option B.