If the $n^{th}$ term of an arithmetic progression is $3n - 1$,then the sum of its first five terms is.......

The sequence $\frac{5}{\sqrt{7}}, \frac{6}{\sqrt{7}}, \sqrt{7}, \dots$ is

If $\log 2$,$\log (2^x - 1)$,and $\log (2^x + 3)$ are in arithmetic progression,then the value of $x$ is:

If the sum of the first $21$ terms of the series $\log _{9^{1 / 2}} x + \log _{9^{1 / 3}} x + \log _{9^{1 / 4}} x + \dots$ where $x > 0$ is $504$,then $x$ is equal to:

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 $a_1, a_2, a_3, \ldots$ be in an $A.P.$ such that $\sum_{k=1}^{12} a_{2k-1} = -\frac{72}{5} a_1$,where $a_1 \neq 0$. If $\sum_{k=1}^{n} a_k = 0$,then $n$ is: