The sum of first two terms of a $G.P.$ is $1$ and every term of this series is twice of its previous term, then the first term will be
$1/4$
$1/3$
$2/3$
$3/4$
If ${\log _a}x,\;{\log _b}x,\;{\log _c}x$ be in $H.P.$, then $a,\;b,\;c$ are in
The first term of a $G.P.$ is $7$, the last term is $448$ and sum of all terms is $889$, then the common ratio is
Show that the ratio of the sum of first $n$ terms of a $G.P.$ to the sum of terms from
$(n+1)^{ th }$ to $(2 n)^{ th }$ term is $\frac{1}{r^{n}}$
If the first term of a $G.P. a_1, a_2, a_3......$ is unity such that $4a_2 + 5a_3$ is least, then the common ratio of $G.P.$ is
If $s$ is the sum of an infinite $G.P.$, the first term $a$ then the common ratio $r$ given by