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
$\frac{y}{x}$
$\frac{x}{y}$
$xy$
$\sqrt {xy} $
If $a,\;b,\;c$ are in $A.P.$, then ${3^a},\;{3^b},\;{3^c}$ shall be in
If $2^{10}+2^{9} \cdot 3^{1}+28 \cdot 3^{2}+\ldots+2 \cdot 3^{9}+3^{10}=S -211$ then $S$ is equal to
A $G.P.$ consists of an even number of terms. If the sum of all the terms is $5$ times the sum of terms occupying odd places, then find its common ratio.
If $a,\;b,\;c$ are in $A.P.$, $b,\;c,\;d$ are in $G.P.$ and $c,\;d,\;e$ are in $H.P.$, then $a,\;c,\;e$ are in
If $b$ is the first term of an infinite $G.P$ whose sum is five, then $b$ lies in the interval