Question

Find the common ratio in the following G.P. $\sqrt{3},3,3\sqrt{3}$ ...........

Answer 1

We know that the common ratio of a geometric progression is $r=\frac{T_2}{T_1}$ where $T_1$ is the first term and $T_2$ is the second term of G.P.

It is given that the first term of G.P is $T_1=\sqrt{3}$ and the second term is $T_2=3$, therefore,

$r=\frac{T_2}{T_1}=\frac{3}{\sqrt{3}}=\frac{\sqrt{3}\times \sqrt{3}}{\sqrt{3}}=\sqrt{3}$

Hence, the common ratio is $\sqrt{3}$.