Question

Second term of a geometric progression is 6 and its fifth term is 9 times of its third term. Find the geometric progression. Consider that each term of the G.P. is positive.

Answer 1

Second term of GP = 6
ar = 6

fifth term=$9\times \left(thirdterm\right)$

$a{r}^4=9\times a{r}^2$

$\frac{a{r}^4}{a{r}^2}$ = 9

$r^2$ = 9

r = √9 = +-3

consider GP is positive therefor r = 3

ar = 6
a = $\frac{6}{3}$ = 2

therefore GP is
$a,ar,a{r}^2....$

2 , 6 , 18 , 54.....