If $x, G_1, G_2, y$ are the consecutive terms of a $G.P.$,then the value of $G_1 G_2$ is

The sum of the first four terms of a geometric progression $(G.P.)$ is $\frac{65}{12}$ and the sum of their respective reciprocals is $\frac{65}{18}$. If the product of the first three terms of the $G.P.$ is $1$,and the third term is $\alpha$,then $2\alpha$ is ....... .

Evaluate $\sum\limits_{k = 1}^{11} {\left( {2 + {3^k}} \right)} $

If the ratio of the sum of the first three terms and the sum of the first six terms of a $G.P.$ is $125 : 152$,then the common ratio $r$ is:

If the first term of a $G.P.$ is $5$ and the common ratio is $-5$,then which term is $3125$ (in $^{th}$)?

For a $G.P.$,if $(m+n)^{\text{th}}$ term is $p$ and $(m-n)^{\text{th}}$ term is $q$,then the $m^{\text{th}}$ term is $.........$