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

Answer:

Step-by-step explanation:

Answer 2

Let the 4 numbers are
$\frac{a}{ {r}^{2} } ,\: \: \frac{a}{r} ,\: a,\: ar ,\: \: a{r}^{2}$
now according to the question,there product is 1:

$\frac{a}{ {r}^{2}} \times \frac{a}{r} \times a\times ar \times a{r}^{2} = 32\\ \\ {a}^{5} ={2}^{5} \\ \\ a = 2$
product of fourth and fifth term

$a{r}^{2}\times ar = 108 \\ \\ put \: a = 2\\ \\ {a}^{2}r^{3}= 108\\ \\ 4r^{3}= 108 \\ \\ r^{3}=\frac{108}{4} \\ \\ r^{3} =27\\ \\r^{3}=3^{3}\\\\r=3$

So 5 numbers are

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

Hope it helps you.