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

If the roots of the equation $4x^3 - 12x^2 + 11x + k = 0$ are in arithmetic progression,then $k$ is equal to

If $a_1, a_2, a_3, ......., a_n$ are in $A.P.$,where $a_i > 0$ for all $i$,then the value of $\frac{1}{\sqrt{a_1} + \sqrt{a_2}} + \frac{1}{\sqrt{a_2} + \sqrt{a_3}} + ....... + \frac{1}{\sqrt{a_{n-1}} + \sqrt{a_n}} = $

The sequence $\log a, \log \frac{a^2}{b}, \log \frac{a^3}{b^2}, \ldots$ is

Suppose $a_1, a_2, a_3, \ldots, a_{2012}$ are integers arranged on a circle. Each number is equal to the average of its two adjacent numbers. If the sum of all even-indexed numbers is $3018$,what is the sum of all numbers?

If the sum of a certain number of terms of the $A.P.$ $25, 22, 19, \ldots$ is $116$,find the last term.