Let $a_{n}$ be the $n^{\text {th }}$ term of a G.P. of positive terms.
If $\sum\limits_{n=1}^{100} a_{2 n+1}=200$ and $\sum\limits_{n=1}^{100} a_{2 n}=100,$ then $\sum\limits_{n=1}^{200} a_{n}$ is equal to
$225$
$175$
$300$
$150$
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
The value of $0.\mathop {234}\limits^{\,\,\, \bullet \,\, \bullet } $ is
If the first term of a $G.P.$ ${a_1},\;{a_2},\;{a_3},..........$ is unity such that $4{a_2} + 5{a_3}$ is least, then the common ratio of $G.P.$ is
The $G.M.$ of roots of the equation ${x^2} - 18x + 9 = 0$ is
How many terms of the $G.P.$ $3, \frac{3}{2}, \frac{3}{4}, \ldots$ are needed to give the sum $\frac{3069}{512} ?$