Question

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

Answer 1

Let a be the first term and r be the common ratio of the given G.P.

$\therefore$ p = 5th term

$\Rightarrow p=a{r}^4$ ........(i)

q = 8th term

$\Rightarrow q=a{r}^7$ ....... (ii)

s = 11th

$\Rightarrow s=a{r}^{10}$

Now, q^2 = $(a{r}^7{)}^2=a^2{r}^{14}$

$\Rightarrow \left(a{r}^4\right)\left(a{r}^{10}\right)=px$ [From (i) and (iii)]

$\therefore q^2=ps$