If ${x_r} = \cos (\pi /{3^r}) - i\sin (\pi /{3^r}),$ (where $i = \sqrt{-1}),$ then value of $x_1.x_2.x_3......\infty ,$ is :-
$1$
$-1$
$-i$
$i$
The sum of $3$ numbers in geometric progression is $38$ and their product is $1728$. The middle number is
Let the first term $a$ and the common ratio $r$ of a geometric progression be positive integers. If the sum of its squares of first three terms is $33033$, then the sum of these three terms is equal to
If in an infinite $G.P.$ first term is equal to the twice of the sum of the remaining terms, then its common ratio is
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
Find a $G.P.$ for which sum of the first two terms is $-4$ and the fifth term is $4$ times the third term.