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

Show that the sum of $(m+n)^{th}$ and $(m-n)^{th}$ terms of an $A.P.$ is equal to twice the $m^{th}$ term.

If the roots of the equation $6x^3-11x^2+6x-1=0$ are in harmonic progression,then the roots of $x^3-6x^2+11x-6=0$ will be in

Let ${a_1}, {a_2}, \dots, {a_{30}}$ be an $A.P.$,$S = \sum_{i=1}^{30} {a_i}$ and $T = \sum_{i=1}^{15} {a_{2i-1}}$. If ${a_5} = 27$ and $S - 2T = 75$,then ${a_{10}}$ is equal to:

Given an $A.P.$ whose terms are all positive integers. The sum of its first nine terms is greater than $200$ and less than $220$. If the second term is $12$,then its $4^{th}$ term is: