Question

Three numbers are in G.P. Their sum is $28$ and their product is $512$. The numbers are :

• A. $6,9$ and $13$
• B. $4,8$ and $16$
• C. $2,8$ and $18$
• D. $2,6$ and $18$

Answer 1

Answer: (B)

$4,8$ and $16$

Let the three numbers be $a,ar,$ $a{r}^2$,
where $r$ is the common ratio.
$\Rightarrow a+ar+a{r}^2=28$ and $a^3{r}^3=512$
$\Rightarrow ar=8\Rightarrow a+a{r}^2=20$
$\Rightarrow 8r^2-20r+8=0$
$\Rightarrow r=2,r=\frac{1}{2}$
If $r=2,a=4$
Therefore, the three numbers are $4,8,16$.