The sum of $3$ numbers in geometric progression is $38$ and their product is $1728$. The middle number is

Let ${S_n}$ denote the sum of $n$ terms of an $A.P.$ If ${S_{2n}} = 3{S_n}$,then the ratio $\frac{{{S_{3n}}}}{{{S_n}}}$ is equal to:

If the $10^{\text{th}}$ term of an $A$.$P$. is $\frac{1}{20}$ and its $20^{\text{th}}$ term is $\frac{1}{10}$,then the sum of its first $200$ terms is

The $H.M.$ between the roots of the equation $x^2 - 10x + 11 = 0$ is

$A$ ball rolling up an incline covers $36\, m$ during the first second,$32\, m$ during the second,$28\, m$ during the next and so on. How much distance will it travel during the $8^{th}$ second? (in $m$)

The two geometric means between the numbers $1$ and $64$ are