The sum of the numbers between $100$ and $1000$ which are divisible by $9$ is:

If the $4^{th}, 7^{th}$ and $10^{th}$ terms of a $G.P.$ are $a, b, c$ respectively,then the relation between $a, b, c$ is

Let $S_k = \frac{1 + 2 + 3 + .... + k}{k}$. If $S_1^2 + S_2^2 + ....... + S_{10}^2 = \frac{5}{12}A$,then $A$ is equal to

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

Let $a, b$ and $c$ be in $G.P.$ with common ratio $r,$ where $a \ne 0$ and $0 < r \le \frac{1}{2}.$ If $3a, 7b$ and $15c$ are the first three terms of an $A.P.,$ then the $4^{th}$ term of this $A.P.$ is

For all positive integral values of $n$,the value of $3 \cdot 1 \cdot 2 + 3 \cdot 2 \cdot 3 + 3 \cdot 3 \cdot 4 + \dots + 3 \cdot n \cdot (n + 1)$ is