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

There are $15$ terms in an arithmetic progression. Its first term is $5$ and their sum is $390$. The middle term is

If the sum of the first $n$ terms of a sequence is of the form $An^2 + Bn$,where $A$ and $B$ are constants independent of $n$,then the sequence is a ........

Find the $17^{\text{th}}$ and $24^{\text{th}}$ term in the following sequence whose $n^{\text{th}}$ term is $a_{n} = 4n - 3$.

If the roots of the equation $x^3 - 9x^2 + \alpha x - 15 = 0$ are in $A.P.$,then $\alpha$ is:

If $100$ times the $100^{th}$ term of an Arithmetic Progression with a non-zero common difference is equal to $50$ times its $50^{th}$ term,then what is its $150^{th}$ term?