Question

The sum of three numbers in $G.P.$ is $42$. If the first two numbers are increased by $2$ and third is decreased by $4$, the resulting numbers form an $A.P.$ Find the numbers of $G.P.$

Answer 1

Proceed as in part $\left(a\right)$
$2r^2-5r+2=0$ $\Rightarrow r=2,\frac{1}{2}$
And corresponding values of $a$ are $6,24$. Hence the numbers are $6,12,24,$ or $24,12,6$.