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

For a sequence $,a_1 = 2$ and $\frac{a_{n+1}}{a_n} = \frac{1}{3}.$ Then $\sum_{r=1}^{20} a_r $is

Find the $n^{th}$ term of the following series: $5, 14, 29, 50, 77, \ldots$

If $a, b, c, d, e$ are in $A.P.$,then the value of $a + b + 4c - 4d + e$ in terms of $a$,if possible,is:

If $f(x + y, x - y) = xy$,then the arithmetic mean of $f(x, y)$ and $f(y, x)$ is

The common difference of the $A.P.$ $b_{1}, b_{2}, \ldots, b_{m}$ is $2$ more than the common difference of $A.P.$ $a_{1}, a_{2}, \ldots, a_{n}.$ If $a_{40} = -159,$ $a_{100} = -399$ and $b_{100} = a_{70},$ then $b_{1}$ is equal to