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 ${(p + q)^{th}}$ term of a $G.P.$ be $m$ and ${(p - q)^{th}}$ term be $n$, then the ${p^{th}}$ term will be
If ${G_1}$ and ${G_2}$ are two geometric means and $A$ the arithmetic mean inserted between two numbers, then the value of $\frac{{G_1^2}}{{{G_2}}} + \frac{{G_2^2}}{{{G_1}}}$is
Let $a_{n}$ be the $n^{\text {th }}$ term of a G.P. of positive terms.
If $\sum\limits_{n=1}^{100} a_{2 n+1}=200$ and $\sum\limits_{n=1}^{100} a_{2 n}=100,$ then $\sum\limits_{n=1}^{200} a_{n}$ is equal to
Three numbers are in $G.P.$ such that their sum is $38$ and their product is $1728$. The greatest number among them is
If $(y - x),\,\,2(y - a)$ and $(y - z)$ are in $H.P.$, then $x - a,$ $y - a,$ $z - a$ are in