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
$1$
$2$
$1/3$
$-1/3$
An $A.P.$, a $G.P.$ and a $H.P.$ have the same first and last terms and the same odd number of terms. The middle terms of the three series are in
If $x$ is added to each of numbers $3, 9, 21$ so that the resulting numbers may be in $G.P.$, then the value of $x$ will be
If ${G_1}$ and ${G_2}$ are two geometric means and $A$ the arithmetic mean inserted between two numbers, then the value of $\frac{{G_1^2}}{{{G_2}}} + \frac{{G_2^2}}{{{G_1}}}$is
The sum of the series $3 + 33 + 333 + ... + n$ terms is
If ${\log _a}x,\;{\log _b}x,\;{\log _c}x$ be in $H.P.$, then $a,\;b,\;c$ are in