The $G.M.$ of the roots of the equation $x^2 - 18x + 9 = 0$ is

If every term of a $G.P.$ with positive terms is the sum of its two previous terms,then the common ratio of the series is

The sum of $n$ terms of the following series $1 + (1 + x) + (1 + x + x^2) + \dots$ will be

Let ${T_r}$ be the ${r^{th}}$ term of an $A.P.$ for $r = 1, 2, 3, ....$. If for some positive integers $m, n$ we have ${T_m} = \frac{1}{n}$ and ${T_n} = \frac{1}{m}$,then ${T_{mn}}$ equals

Three numbers are in $G.P.$ such that their sum is $38$ and their product is $1728$. The greatest number among them is

After inserting $n$ arithmetic means $(A.M.s)$ between $2$ and $38$,the sum of the resulting progression is $200$. The value of $n$ is