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

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

The sum of $24$ terms of the following series $\sqrt 2 + \sqrt 8 + \sqrt {18} + \sqrt {32} + .........$ is

Show that the sum of $(m+n)^{ th }$ and $(m-n)^{ th }$ terms of an $A.P.$ is equal to twice the $m^{\text {th }}$ term.

If $\log 2,\;\log ({2^n} - 1)$ and $\log ({2^n} + 3)$ are in $A.P.$, then $n =$

If three positive numbers $a, b$ and $c$ are in $A.P.$ such that $abc\, = 8$, then the minimum possible value of $b$ is