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

The ratio of the sum of $m$ and $n$ terms of an $A.P.$ is $m^2:n^2$. Then the ratio of the $m^{th}$ and $n^{th}$ term will be:

Let $S_n$ be the sum of all integers $k$ such that $2^n < k < 2^{n+1}$,for $n \geq 1$. Then,$9$ divides $S_n$ if and only if

If the sum of the first $n$ terms of an $A.P.$ is $cn(n - 1)$,where $c \neq 0$,then the sum of the squares of these terms is:

If $p$ times the $p^{th}$ term of an arithmetic progression is equal to $q$ times its $q^{th}$ term,then the $(p + q)^{th}$ term of this progression is........

If $a_1, a_2, a_3, . . . , a_n, . . .$ are in $A.P.$ such that $a_4 - a_7 + a_{10} = m$,then the sum of the first $13$ terms of this $A.P.$ is .............. $m$.