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
$225$
$175$
$300$
$150$
Three numbers are in $G.P.$ such that their sum is $38$ and their product is $1728$. The greatest number among them is
The number which should be added to the numbers $2, 14, 62$ so that the resulting numbers may be in $G.P.$, is
If $1\, + \,\sin x\, + \,{\sin ^2}x\, + \,...\infty \, = \,4\, + \,2\sqrt 3 ,\,0\, < \,x\, < \,\pi $ then
The first term of an infinite geometric progression is $x$ and its sum is $5$. Then
If $S$ is the sum to infinity of a $G.P.$, whose first term is $a$, then the sum of the first $n$ terms is