Find the geometric mean of the first $n$ natural numbers.

If $4^{\text{th}}$,$10^{\text{th}}$,and $16^{\text{th}}$ terms of a $G$.$P$. are $x, y$,and $z$ respectively,then

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

If $a, b, c$ are the $p^{th}, q^{th}$ and $r^{th}$ terms of a $G.P.$,then $\left( \frac{c}{b} \right)^p \left( \frac{b}{a} \right)^r \left( \frac{a}{c} \right)^q$ is equal to

If $p, q, r$ are in a geometric progression and $a, b, c$ are in another geometric progression,then $cp, bq, ar$ are in...

$A$ person has $2$ parents,$4$ grandparents,$8$ great-grandparents,and so on. Find the total number of his ancestors during the $10$ generations preceding his own.