WAEC 2023 · Paper 1 · Q10

An exponential sequence (G.P.) is given by $\frac{9}{2}, \frac{3}{4}, \frac{1}{8}, \ldots$ . Find its sum to infinity.

Worked solution (try it first)

The first term is $a = \frac{9}{2}$ and the common ratio is $r = \frac{3}{4} \div \frac{9}{2}$
$= \frac{1}{6}$ .
Since $|r| < 1$ , the sum to infinity is $S_\infty = \dfrac{a}{1 - r}$
$= \dfrac{9/2}{5/6}$ .
Work it out: $\frac{9}{2} \times \frac{6}{5} = \frac{27}{5}$
$= 5\frac{2}{5}$ , option B.