Question

The 5th, 8th and 11th terms of a G.P are $p,q$ and $s$ respectively. Show that $q^2=ps$

Answer 1

$a_5=p=a_1{r}^4$

$a_8=q=a_1{r}^7$

$a_{1}1=s=a_1{r}^{10}$

$q^2=a_1^2{r}^{14}$

$q^2=a_1{r}^4.a_1{r}^{10}$

$q^2=ps$