In an arithmetic progression,if $S_{40} = 1030$ and $S_{12} = 57$,then $S_{30} - S_{10}$ is equal to:

If $a, b, c, d, e, f$ are in $A.P.$,then the value of $e - c$ is

The sum of $24$ terms of the following series $\sqrt{2} + \sqrt{8} + \sqrt{18} + \sqrt{32} + \dots$ is

$A$ man saves $200$ rupees in each of the first three months of his job. In the subsequent months,his savings increase by $40$ rupees compared to the previous month. After how many months from the start of the job will his total savings be $11040$ rupees?

Suppose the sum of the first $m$ terms of an arithmetic progression is $n$ and the sum of its first $n$ terms is $m$,where $m \neq n$. Then,the sum of the first $(m+n)$ terms of the arithmetic progression is

If the first term of an $A.P.$ is $3$ and the sum of its first four terms is equal to one-fifth of the sum of the next four terms,then the sum of the first $20$ terms is equal to