The sum of an infinite geometric series is 6.

Given: $\frac{a}{1-r}=6, a=2$

To find: $r=$ ?

$\therefore \frac{2}{1-r}=6$

$\Rightarrow 1-r=\frac{2}{6}=\frac{1}{3}$

$\Rightarrow 3(1-r)=1$

$\Rightarrow 3-3 r=1$

$\Rightarrow 3 r=3-1$

$\Rightarrow r=\frac{2}{3}$

Common ratio $r=\frac{2}{3}$