If the sum and product of the first three terms in an $A.P.$ are $33$ and $1155$,respectively,then a value of its $11^{th}$ term 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 $T_{mn} = \dots$

If the ratio of the sum of $n$ terms of two arithmetic progressions is $(7n + 1) : (4n + 27)$,then what is the ratio of their $11^{th}$ terms?

Given that $n$ arithmetic means are inserted between two sets of numbers $(a, 2b)$ and $(2a, b)$, where $a, b \in \mathbb{R}$. Suppose the $m^{th}$ means between these sets are equal, then the ratio $a : b$ is equal to:

The median of all $4$-digit numbers that are divisible by $7$ is

If twice the $11^{th}$ term of an $A.P.$ is equal to $7$ times its $21^{st}$ term,then its $25^{th}$ term is equal to