The two geometric means between the number $1$ and $64$ are
$1$ and $64$
$4$ and $16$
$2$ and $16$
$8$ and $16$
If $x, {G_1},{G_2},\;y$ be the consecutive terms of a $G.P.$, then the value of ${G_1}\,{G_2}$ will be
The G.M. of the numbers $3,\,{3^2},\,{3^3},\,......,\,{3^n}$ is
If $y = x + {x^2} + {x^3} + .......\,\infty ,\,{\rm{then}}\,\,x = $
Insert three numbers between $1$ and $256$ so that the resulting sequence is a $G.P.$
For a sequence $ < {a_n} > ,\;{a_1} = 2$ and $\frac{{{a_{n + 1}}}}{{{a_n}}} = \frac{1}{3}$. Then $\sum\limits_{r = 1}^{20} {{a_r}} $ is