Question

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

Answer 1

Let 'a' be the first term and 'r' be the common ratio of the gecen A.P

Here, $a_5=p\Rightarrow a{r}^4=p$

$a_8=p\Rightarrow a{r}^7=q$

$a_{11}=p\Rightarrow a{r}^{11}=s$

Squaring both sides of equation (2), we get

$q^2=(a{r}^7{)}^2\Rightarrow q^2=a^2{r}^{14}$

$\Rightarrow q^2=\left(a{r}^4\right)\left(a{r}^{10}\right)$

$\Rightarrow q^2=ps[\therefore p=a{r}^{4}ands=a{r}^{10}]$