Let $3,6,9,12, \ldots$ upto $78$ terms and $5,9,13,17, \ldots$ upto $59$ terms be two series. Then, the sum of the terms common to both the series is equal to

If $n$ arithmetic means are inserted between a and $100$ such that the ratio of the first mean to the last mean is $1: 7$ and $a+n=33$, then the value of $n$ is

If the sum of first $p$ terms of an $A.P.$ is equal to the sum of the first $q$ terms, then find the sum of the first $(p+q)$ terms.

If the sum of the first $n$ terms of a series be $5{n^2} + 2n$, then its second term is

The difference between an integer and its cube is divisible by

${7^{th}}$ term of an $A.P.$ is $40$, then the sum of first $13$ terms is