JAMB 1998 · UME · Q20

The sum of the first three terms of a geometric progression is half its sum to infinity. Find the positive common ratio of the progression.

Worked solution (try it first)

The sum of three terms is $\dfrac{a(1 - r^3)}{1 - r}$ and the sum to infinity is $\dfrac{a}{1 - r}$ .
Set the first equal to half the second and cancel $\dfrac{a}{1 - r}$ : $1 - r^3 = \frac12$ .
So $r^3 = \frac12$ , and taking the cube root gives $r = \dfrac{1}{\sqrt[3]{2}}$ , option D.