If the sum of $n$ terms of an $A$.$P$. is $3n^2 + 5n$ and its $m$th term is $164$, then the value of $m$ is

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:

Let $a_n, n \geq 1$,be an arithmetic progression with first term $2$ and common difference $4$. Let $M_n$ be the average of the first $n$ terms. Then the sum $\sum_{n=1}^{10} M_n$ is

If $1, \log _9(3^{1-x}+2), \log _3(4 \cdot 3^x-1)$ are in $A.P.$, then $x$ equals

If the sum of the first $p$ terms of an $A.P.$ is equal to the sum of the first $q$ terms,then find the sum of the first $(p+q)$ terms.

The natural numbers are arranged in rows as follows:
$1$
$2, 3$
$4, 5, 6$
$7, 8, 9, 10$
$. . .$
What is the sum of the numbers in the $n^{th}$ row?