Let $a_1, a_2, ..., a_{10}$ be a $G.P.$ If $\frac{a_3}{a_1} = 25$,then $\frac{a_9}{a_5}$ is equal to:

If $A, B, C$ are the $p^{th}, q^{th},$ and $r^{th}$ terms of a $GP$ respectively,then $A^{q-r} \cdot B^{r-p} \cdot C^{p-q} =$

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

If the $p^{\text{th}}$,$q^{\text{th}}$,and $r^{\text{th}}$ terms of a $G.P.$ are $a$,$b$,and $c$ respectively,prove that $a^{q-r} b^{r-p} c^{p-q} = 1$.

If in a geometric progression $\{a_n\}$,$a_1 = 3$,$a_n = 96$ and $S_n = 189$,then the value of $n$ is

If $\log_x a, a^{x/2}$ and $\log_b x$ are in $G.P.$,then $x = $