Question

Let three numbers in G.P. whose sum is $65$ and whose product is $3375$. Find smallest of those numbers.

Answer 1

Three numbers are in G.P.

$\text{Sum}=65$.

And product $=3375$

Let the numbers be $\frac{a}{r},a,ar$.

So, the product is $a^3=3375$.

$\Rightarrow a=15$.
Now $\text{Sum}=65=\frac{15}{r}+15+15r$
$\Rightarrow r+\frac{1}{r}=\frac{10}{3}$

$\Rightarrow r=3$

So, the numbers are $5,15,45$.