Three numbers are in $G.P.$ such that their sum is $38$ and their product is $1728$. The greatest number among them is
$18$
$16$
$14$
None of these
Find the $20^{\text {th }}$ and $n^{\text {th }}$ terms of the $G.P.$ $\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, \ldots$
If the geometric mean between $a$ and $b$ is $\frac{{{a^{n + 1}} + {b^{n + 1}}}}{{{a^n} + {b^n}}}$, then the value of $n$ is
The sum to infinity of the progression $9 - 3 + 1 - \frac{1}{3} + .....$ is
If $1\, + \,\sin x\, + \,{\sin ^2}x\, + \,...\infty \, = \,4\, + \,2\sqrt 3 ,\,0\, < \,x\, < \,\pi $ then
Find the sum of first $n$ terms and the sum of first $5$ terms of the geometric
series $1+\frac{2}{3}+\frac{4}{9}+\ldots$