If the sum of the $n$ terms of $G.P.$ is $S$ product is $P$ and sum of their inverse is $R$, than ${P^2}$ is equal to
$\frac{R}{S}$
$\frac{S}{R}$
${\left( {\frac{R}{S}} \right)^n}$
${\left( {\frac{S}{R}} \right)^n}$
The difference between the fourth term and the first term of a Geometrical Progresssion is $52.$ If the sum of its first three terms is $26,$ then the sum of the first six terms of the progression is
If $a,\;b,\;c$ are ${p^{th}},\;{q^{th}}$ and ${r^{th}}$ terms of a $G.P.$, then ${\left( {\frac{c}{b}} \right)^p}{\left( {\frac{b}{a}} \right)^r}{\left( {\frac{a}{c}} \right)^q}$ is equal to
Insert three numbers between $1$ and $256$ so that the resulting sequence is a $G.P.$
The sum of first four terms of a geometric progression $(G.P.)$ is $\frac{65}{12}$ and the sum of their respective reciprocals is $\frac{65}{18} .$ If the product of first three terms of the $G.P.$ is $1,$ and the third term is $\alpha$, then $2 \alpha$ is ....... .
The sum of a $G.P.$ with common ratio $3$ is $364$, and last term is $243$, then the number of terms is