The $G.M.$ of the numbers $3,\,{3^2},\,{3^3},....,\,{3^n}$ is
${3^{\frac{2}{n}}}$
${3^{\frac{{n + 1}}{2}}}$
${3^{\frac{n}{2}}}$
${3^{\frac{{n - 1}}{2}}}$
If $a,\;b,\;c$ are in $A.P.$, $b,\;c,\;d$ are in $G.P.$ and $c,\;d,\;e$ are in $H.P.$, then $a,\;c,\;e$ are in
If $s$ is the sum of an infinite $G.P.$, the first term $a$ then the common ratio $r$ given by
If $a,\,b,\,c$ are in $G.P.$, then
If the product of three consecutive terms of $G.P.$ is $216$ and the sum of product of pair-wise is $156$, then the numbers will be
Find the sum to indicated number of terms in each of the geometric progressions in $\left.1,-a, a^{2},-a^{3}, \ldots n \text { terms (if } a \neq-1\right)$