$8^{th}$ term of the series $2\sqrt 2 + \sqrt 2 + 0 + .....$ will be

If the sum of the first $2n$ terms of $2,\,5,\,8...$ is equal to the sum of the first $n$ terms of $57,\,59,\,61...$, then $n$ is equal to

${7^{th}}$ term of an $A.P.$ is $40$, then the sum of first $13$ terms is

If the sum of the series $2 + 5 + 8 + 11............$ is $60100$, then the number of terms are

If the sum of the first $n$ terms of the series $\sqrt 3  + \sqrt {75}  + \sqrt {243}  + \sqrt {507}  + ......$ is $435\sqrt 3 $ , then $n$ equals

If $^n{C_4},{\,^n}{C_5},$ and ${\,^n}{C_6},$ are in $A.P.,$ then $n$ can be