If the $9^{th}$ and $19^{th}$ terms of an arithmetic progression are $35$ and $75$ respectively,what is its $20^{th}$ term?

$150$ workers were engaged to finish a piece of work in a certain number of days. $4$ workers dropped the second day,$4$ more workers dropped the third day and so on. It takes eight more days to finish the work now. The number of days in which the work was completed is

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of an Arithmetic Progression are $a$,$b$,and $c$ respectively,then $[a(q - r) + b(r - p) + c(p - q)] = ?$

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:

Let $A, G, H$ and $S$ respectively denote the arithmetic mean,geometric mean,harmonic mean and the sum of the numbers $a_1, a_2, a_3, \ldots, a_n$. Then the value of $x$ at which the function $f(x)=\sum_{k=1}^n(x-a_k)^2$ has a minimum is

If $S_n$ denotes the sum of $n$ terms of an arithmetic progression,then the value of $(S_{2n} - S_n)$ is equal to