# If 5th, 8th and 11th terms of a G.P. are p. q and s respectively,

Question:

If 5th, 8th and 11th terms of a G.P. are pq and s respectively, prove that q2 = ps.

Solution:

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

$\therefore p=5^{\text {th }}$ term

$\Rightarrow p=a r^{4}$    ...(1)

$q=8^{\text {th }}$ term

$\Rightarrow q=a r^{7}$    ...(2)

$s=11^{\text {th }}$

$\Rightarrow s=a r^{10}$    ...(3)

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

$\Rightarrow\left(a r^{4}\right)\left(a r^{10}\right)=p s \quad[$ From $(1)$ and $(3)]$

$\therefore q^{2}=p s$