Find the $10^{\text{th}}$ and $n^{\text{th}}$ terms of the $G.P.$ $5, 25, 125, \ldots$

The roots of the equation $x^3-14x^2+56x-64=0$ are in

The sum of the first ten terms of a geometric progression is $S_1$ and the sum of the next ten terms ($11^{th}$ to $20^{th}$) is $S_2$. What is the common ratio?

If three geometric means are inserted between $2$ and $32$,then the third geometric mean will be

If the $5^{th}$ term of a geometric progression is $2$,what is the product of its first $9$ terms?

Let the positive numbers $a_1, a_2, a_3, a_4$ and $a_5$ be in a $G$.$P$. Let their mean and variance be $\frac{31}{10}$ and $\frac{m}{n}$ respectively,where $m$ and $n$ are co-prime. If the mean of their reciprocals is $\frac{31}{40}$ and $a_3+a_4+a_5=14$,then $m+n$ is equal to $.........$.