The $8^{th}$ term of the series $2\sqrt{2} + \sqrt{2} + 0 + \dots$ will be: (in $\sqrt{2}$)

Three numbers are in $A.P.$ such that their sum is $18$ and the sum of their squares is $158$. The greatest number among them is

Let there be four distinct integers in an increasing arithmetic progression. One of these integers is equal to the sum of the squares of the other three. What is the product of all these numbers?

If $1, \log_9(3^{1-x} + 2), \log_3(4 \cdot 3^x - 1)$ are in an arithmetic progression,then $x = \dots$

If $a$,$b$,and $c$ are the first,second,and last terms of an arithmetic progression respectively,then the total number of terms is......

Let ${a_1}, {a_2}, \dots, {a_{30}}$ be an $A.P.$,$S = \sum_{i=1}^{30} {a_i}$ and $T = \sum_{i=1}^{15} {a_{2i-1}}$. If ${a_5} = 27$ and $S - 2T = 75$,then ${a_{10}}$ is equal to: