Question

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

Answer 1

Formula,

$a_n=a{r}^{n-1}$

Given,

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

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

$a_{11}=a{r}^{10}=r$

LHS:

$q^2$

$=(a{r}^7{)}^2$

$=a^2{r}^{14}$

RHS:

$ps$

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

$=a^2{r}^{14}$

LHS=RHS.