If the $m^{th}$ terms of the series $63 + 65 + 67 + 69 + \dots$ and $3 + 10 + 17 + 24 + \dots$ are equal,then $m = $

Let $S_n$ denote the sum of the first $n$ terms of an arithmetic progression. If $S_{20} = 790$ and $S_{10} = 145$,then $S_{15} - S_5$ is:

Let $\alpha_{1}, \alpha_{2}, \alpha_{3}, \alpha_{4}$ be an $A$.$P$. of four terms such that each term of the $A$.$P$. and its common difference $l$ are integers. If $\alpha_{1}+\alpha_{2}+\alpha_{3}+\alpha_{4}=48$ and $\alpha_{1}\alpha_{2}\alpha_{3}\alpha_{4}+l^{4}=361$, then the largest term of the $A$.$P$. is equal to

If the $n$ terms $a_1, a_2, \ldots, a_n$ are in $A$.$P$. with common difference $r$, then the difference between the mean of their squares and the square of their mean is

If the first term of an $A.P.$ is $3$ and the sum of its first $25$ terms is equal to the sum of its next $15$ terms,then the common difference of this $A.P.$ 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?