The sum of numbers from $250$ to $1000$ which are divisible by $3$ is

The number of terms common to the two A.P.'s $3,7,11, \ldots ., 407$ and $2,9,16, \ldots . .709$ is

Let $S_n$ denote the sum of first $n$ terms an arithmetic progression. If $S_{20}=790$ and $S_{10}=145$, then $S_{15}-$ $S_5$ is:

How many terms of the $A.P.$ $-6,-\frac{11}{2},-5, \ldots \ldots$ are needed to give the sum $-25 ?$

Let $A =\left\{1, a _{1}, a _{2} \ldots \ldots a _{18}, 77\right\}$ be a set of integers with $1< a _{1}< a _{2}<\ldots \ldots< a _{18}<77$. Let the set $A + A =\{ x + y : x , y \in A \} \quad$ contain exactly $39$ elements. Then, the value of $a_{1}+a_{2}+\ldots \ldots+a_{18}$ is equal to...........

Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=\frac{2 n-3}{6}$