If the first,second and last terms of an $A.P.$ are $a, b$ and $2a$ respectively,then its sum is:

Let $T_r$ be the $r^{\text{th}}$ term of an $A.P.$ If for some $m$,$T_m = \frac{1}{25}$,$T_{25} = \frac{1}{20}$ and $20 \sum_{r=1}^{25} T_r = 13$,then $5m \sum_{r=m}^{2m} T_r$ is equal to:

$A$ man saves $200$ in each of the first three months of his service. In each of the subsequent months, his saving increases by $40$ compared to the saving of the immediately previous month. His total saving from the start of service will be $11040$ after ............ months.

If the sum of the first $n$ terms of an arithmetic progression is $cn^2$,what is the sum of the squares of these $n$ terms?

If $A$ is an arithmetic mean between two numbers and $S$ is the sum of $n$ arithmetic means between the same two numbers,then:

If the sides of a right-angled triangle are in an arithmetic progression,then they are in the ratio of.........