The sum of the numbers between $100$ and $1000$, which is divisible by $9$ will be

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

Find the $9^{\text {th }}$ term in the following sequence whose $n^{\text {th }}$ term is $a_{n}=(-1)^{n-1} n^{3}$

In an $A.P.,$ if $p^{\text {th }}$ term is $\frac{1}{q}$ and $q^{\text {th }}$ term is $\frac{1}{p},$ prove that the sum of first $p q$ terms is $\frac{1}{2}(p q+1),$ where $p \neq q$

The sums of $n$ terms of two arithmatic series are in the ratio $2n + 3:6n + 5$, then the ratio of their ${13^{th}}$ terms is

Let $a_1 , a_2, a_3, .... , a_n$, be in $A.P$. If $a_3 + a_7 + a_{11} + a_{15} = 72$ , then the sum of its first $17$ terms is equal to