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
$5$
$6$
$7$
$8$
If $a,b,c$ are in $A.P.$, then ${2^{ax + 1}},{2^{bx + 1}},\,{2^{cx + 1}},x \ne 0$ are in
The value of ${a^{{{\log }_b}x}}$, where $a = 0.2,\;b = \sqrt 5 ,\;x = \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + .........$to $\infty $ is
In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of its progression is equals
The G.M. of the numbers $3,\,{3^2},\,{3^3},\,......,\,{3^n}$ is
If the product of three consecutive terms of $G.P.$ is $216$ and the sum of product of pair-wise is $156$, then the numbers will be