Question

Find five numbers in G.P. such that their product is $32$ and the product of fourth and fifth number is $108$

Answer 1

Let the $5$ nos. in $G.P$be $\frac{a}{r^2},\frac{a}{r},a,ar,a{r}^2$

their product $=32$

$\Rightarrow \frac{a}{r^2}\times \frac{a}{r}\times a\times ar\times a{r}^2=32\Rightarrow a^5=32\Rightarrow a=2$

and $ar\times {ar}^2=108\Rightarrow a^2{r}^3=108$

$\Rightarrow 4r^3=108\Rightarrow r^3=27\Rightarrow r=3$

$\therefore$ Required nos. are -$\frac{a}{r^2},\frac{a}{r},a,ar,a{r}^2$

$=\frac{2}{9},\frac{2}{3},2,6,18$