Question

If the product of three consecutive terms of G.P. is 216 and the sum of product of pair-wise is 156, then the numbers will be
[MNR 1978]

• A. 1, 3, 9
• B. 2, 6, 18
• C. 3, 9, 27
• D. 2, 4, 8

Answer 1

The correct option is B

2, 6, 18

Let numbers are $\frac{a}{r}a,ar$
Under conditions, we get $\frac{a}{r}a.ar=216\Rightarrow a=6$
And sum of product pair wise = 156
$\Rightarrow \frac{a}{r}.a+\frac{a}{r}.ar+a.ar=156\Rightarrow r=3$
Hence numbers are 2, 6, 18.

Trick : Since $2\times 6\times 18=216$ (as given) and no other option gives the value.