If $3 + 3\alpha + 3{\alpha ^2} + .........\infty = \frac{{45}}{8}$, then the value of $\alpha $ will be
$15/23$
$7/15$
$7/8$
$15/7$
If $x,\;y,\;z$ are in $G.P.$ and ${a^x} = {b^y} = {c^z}$, then
The product of three geometric means between $4$ and $\frac{1}{4}$ will be
The sum of some terms of $G.P.$ is $315$ whose first term and the common ratio are $5$ and $2,$ respectively. Find the last term and the number of terms.
Let ${a_1},{a_2}...,{a_{10}}$ be a $G.P.$ If $\frac{{{a_3}}}{{{a_1}}} = 25,$ then $\frac {{{a_9}}}{{{a_{ 5}}}}$ equal
Find the sum of $n$ terms in the geometric progression $\sqrt{7}, \sqrt{21}, 3 \sqrt{7}, \ldots$