Let ${a_1},{a_2}...,{a_{10}}$ be a $G.P.$ If $\frac{{{a_3}}}{{{a_1}}} = 25,$ then $\frac {{{a_9}}}{{{a_{ 5}}}}$ equal
$5^4$
$4(5^2)$
$5^3$
$2(5^2)$
If the first and the $n^{\text {th }}$ term of a $G.P.$ are $a$ and $b$, respectively, and if $P$ is the product of $n$ terms, prove that $P^{2}=(a b)^{n}$
Insert two numbers between $3$ and $81$ so that the resulting sequence is $G.P.$
Which term of the following sequences:
$\sqrt{3}, 3,3 \sqrt{3}, \ldots$ is $729 ?$
$0.14189189189….$ can be expressed as a rational number
If $A = 1 + {r^z} + {r^{2z}} + {r^{3z}} + .......\infty $, then the value of $r$ will be