If in a $G.P.$ of $64$ terms, the sum of all the terms is $7$ times the sum of the odd terms of the $G.P,$ then the common ratio of the $G.P$. is equal to
$7$
$4$
$5$
$6$
The number $111..............1$ ($91$ times) is a
Consider an infinite $G.P. $ with first term a and common ratio $r$, its sum is $4$ and the second term is $3/4$, then
If $\frac{a+b x}{a-b x}=\frac{b+c x}{b-c x}=\frac{c+d x}{c-d x}(x \neq 0),$ then show that $a, b, c$ and $d$ are in $G.P.$
If $x > 1,\;y > 1,z > 1$ are in $G.P.$, then $\frac{1}{{1 + {\rm{In}}\,x}},\;\frac{1}{{1 + {\rm{In}}\,y}},$ $\;\frac{1}{{1 + {\rm{In}}\,z}}$ are in
Insert three numbers between $1$ and $256$ so that the resulting sequence is a $G.P.$