JAMB 2003 · UME · Q21

Three consecutive terms of a geometric progression are $n - 2$ , $n$ and $n + 3$ . Find the common ratio.

Worked solution (try it first)

For a G.P., the middle term squared equals the product of the outer two: $n^2 = (n - 2)(n + 3)$ .
Expand: $n^2 = n^2 + n - 6$ , so $n = 6$ .
The terms are 4, 6 and 9, so the common ratio is $6 \div 4 = \frac32$ , option B.