If $n$ geometric means be inserted between $a$ and $b$ then the ${n^{th}}$ geometric mean will be
$a\,{\left( {\frac{b}{a}} \right)^{\frac{n}{{n - 1}}}}$
$a\,{\left( {\frac{b}{a}} \right)^{\frac{{n - 1}}{n}}}$
$a\,{\left( {\frac{b}{a}} \right)^{\frac{n}{{n + 1}}}}$
$a\,{\left( {\frac{b}{a}} \right)^{\frac{1}{n}}}$
The sum of first three terms of a $G.P.$ is $\frac{39}{10}$ and their product is $1 .$ Find the common ratio and the terms.
The sum of the $3^{rd}$ and the $4^{th}$ terms of a $G.P.$ is $60$ and the product of its first three terms is $1000$. If the first term of this $G.P.$ is positive, then its $7^{th}$ term is
If the sum of the series $1 + \frac{2}{x} + \frac{4}{{{x^2}}} + \frac{8}{{{x^3}}} + ....\infty $ is a finite number, then
Find the sum up to $20$ terms in the geometric progression $0.15,0.015,0.0015........$
Which term of the following sequences:
$\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \ldots$ is $\frac{1}{19683} ?$