If the third term of a $G.P.$ is $4$,then the product of its first $5$ terms is:

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

The geometric series $a + ar + ar^2 + ar^3 + \dots \infty$ has a sum of $7$,and the sum of the terms involving odd powers of $r$ is $3$. Then the value of $(a^2 - r^2)$ is -

Show that the ratio of the sum of the first $n$ terms of a $G.P.$ to the sum of the terms from the $(n+1)^{th}$ to the $(2n)^{th}$ term is $\frac{1}{r^{n}}$.

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

If the sum and product of four positive consecutive terms of a $G.P.$ are $126$ and $1296$ respectively,then the sum of common ratios of all such $G.P.s$ is $.........$.