JAMB 1999 · UME · Q12

Sequences & series (AP, GP)

The first term of a geometric progression is twice its common ratio. Find the sum of the first two terms of the progression if its sum to infinity is 8.

Worked solution (try it first)

Put $a = 2r$ into $S_\infty = \dfrac{a}{1 - r} = 8$ : $2r = 8(1 - r)$ .
So $10r = 8$ , giving $r = \frac45$ and $a = \frac85$ .
The second term is $ar = \frac85 \times \frac45$
$= \frac{32}{25}$ .
So the first two terms add up to $\frac{40}{25} + \frac{32}{25} = \frac{72}{25}$ , option C.

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