If the sum of first $n$ terms of an $A.P.$ be equal to the sum of its first $m$ terms, $(m \ne n)$, then the sum of its first $(m + n)$ terms will be

The number of terms of the $A.P. 3,7,11,15...$ to be taken so that the sum is $406$ is

For three positive integers $p , q , r , x ^{ pq p ^2}= y ^{ qr }= z ^{ p ^2 r }$ and $r=p q+1$ such that $3,3 \log _y x, 3 \log _z y, 7 \log _x z$ are in A.P. with common difference $\frac{1}{2}$. Then $r - p - q$ is equal to

The sum of the common terms of the following three arithmetic progressions.

$3,7,11,15,...................,399$

$2,5,8,11,............,359$ and

$2,7,12,17,...........,197$, is equal to $................$.

The sum of all natural numbers between $1$ and $100$ which are multiples of $3$ is

If $\left\{a_{i}\right\}_{i=1}^{n}$ where $n$ is an even integer, is an arithmetic progression with common difference $1$ , and $\sum \limits_{ i =1}^{ n } a _{ i }=192, \sum \limits_{ i =1}^{ n / 2} a _{2 i }=120$, then $n$ is equal to