If the sum of $n$ terms of an arithmetic progression is $3n^2 + 5n$ and $T_m = 164$,then $m = \dots$

Let $x_n, y_n, z_n, w_n$ denote the $n^{th}$ terms of four different arithmetic progressions with positive terms. If $x_4 + y_4 + z_4 + w_4 = 8$ and $x_{10} + y_{10} + z_{10} + w_{10} = 20$,then the maximum value of $x_{20} \cdot y_{20} \cdot z_{20} \cdot w_{20}$ is:

What is the sum of $n$ arithmetic means between $a$ and $b$?

If $\log_{3} 2, \log_{3} (2^{x} - 5)$ and $\log_{3} (2^{x} - \frac{7}{2})$ are in an Arithmetic Progression $(AP)$,then $x = \dots$

Let $S_n$ denote the sum of the first $n$ terms of an arithmetic progression. If $S_{20} = 790$ and $S_{10} = 145$,then $S_{15} - S_5$ is:

If $\frac{3 + 5 + 7 + \dots \text{ to } n \text{ terms}}{5 + 8 + 11 + \dots \text{ to } 10 \text{ terms}} = 7$,then the value of $n$ is