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
$1$
$2$
$1/3$
$-1/3$
If $G$ be the geometric mean of $x$ and $y$, then $\frac{1}{{{G^2} - {x^2}}} + \frac{1}{{{G^2} - {y^2}}} = $
If $x, {G_1},{G_2},\;y$ be the consecutive terms of a $G.P.$, then the value of ${G_1}\,{G_2}$ will be
The sum of first three terms of a $G.P.$ is $\frac{13}{12}$ and their product is $-1$ Find the common ratio and the terms.
The sum to infinity of the progression $9 - 3 + 1 - \frac{1}{3} + .....$ is
How many terms of $G.P.$ $3,3^{2}, 3^{3}$... are needed to give the sum $120 ?$