In a $G.P.$,the first term is $7$,the last term is $448$,and the sum is $889$. Find the common ratio.

Maximum value of the sum of the Arithmetic Progression $50, 48, 46, 44, \dots$ is

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of an arithmetic sequence are $a$,$b$,and $c$ respectively,then the value of $[a(q - r) + b(r - p) + c(p - q)]$ is:

The sum of the first $n$ terms of an $A.P.$ is given by $S_n = 2n + 3n^2$. Another $A.P.$ is formed with the same first term and double the common difference. The sum of the first $n$ terms of this new $A.P.$ is:

The $G.M.$ of the numbers $3, 3^2, 3^3, ..., 3^n$ is

The sum to infinity of the progression $9 - 3 + 1 - \frac{1}{3} + .....$ is