$2.\mathop {357}\limits^{ \bullet \,\, \bullet \,\, \bullet } = $
$\frac{{2355}}{{1001}}$
$\frac{{2370}}{{997}}$
$\frac{{2355}}{{999}}$
None of these
If the ${10^{th}}$ term of a geometric progression is $9$ and ${4^{th}}$ term is $4$, then its ${7^{th}}$ term is
If $\frac{6}{3^{12}}+\frac{10}{3^{11}}+\frac{20}{3^{10}}+\frac{40}{3^{9}}+\ldots . .+\frac{10240}{3}=2^{ n } \cdot m$, where $m$ is odd, then $m . n$ is equal to
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 in a geometric progression $\left\{ {{a_n}} \right\},\;{a_1} = 3,\;{a_n} = 96$ and ${S_n} = 189$ then the value of $n$ is