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

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

Let the terms of an arithmetic progression be $a_1, a_2, a_3, \dots$. If $\frac{a_1 + a_2 + \dots + a_p}{a_1 + a_2 + \dots + a_q} = \frac{p^2}{q^2}$,where $p \neq q$,then $\frac{a_6}{a_{21}} = \dots$

Three numbers are in $A.P.$ whose sum is $33$ and product is $792$. The smallest number among these is:

The $15^{th}$ term of the arithmetic progression $4 + 9 + 14 + 19 + \dots$ is......

Let $T_r$ be the $r$-th term of an arithmetic progression for $r = 1, 2, 3, \dots$. If for some positive integers $m$ and $n$,$T_m = \frac{1}{n}$ and $T_n = \frac{1}{m}$,then $T_{mn} = \dots$