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

Find the sum to the indicated number of terms in the geometric progression: $1, -a, a^{2}, -a^{3}, \ldots$ to $n$ terms (if $a \neq -1$).

If the $n^{th}$ term of the geometric progression $5, - \frac{5}{2}, \frac{5}{4}, - \frac{5}{8}, \dots$ is $\frac{5}{1024}$,then the value of $n$ is:

If $y = x + x^2 + x^3 + \dots \infty$,then $x = $

The sum of a few terms of a geometric series is $728$. If the common ratio is $3$ and the last term is $486$,then the first term of the series will be:

If the roots of $x^3-k x^2+14 x-8=0$ are in geometric progression,then $k$ is equal to