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

Let $a_1, a_2, a_3, \dots, a_n$ be in $A.P$. If $a_3 + a_7 + a_{11} + a_{15} = 72$,then the sum of its first $17$ terms is equal to:

In an $A.P.$,if the $m^{\text{th}}$ term is $n$ and the $n^{\text{th}}$ term is $m$,where $m \neq n$,find the $p^{\text{th}}$ term.

Let $\sum_{k=1}^{n} a_{k} = \alpha n^{2} + \beta n$. If $a_{10} = 59$ and $a_{6} = 7a_{1}$, then $\alpha + \beta$ is equal to:

If $a, b, c$ are in $A.P.$,then $\frac{1}{\sqrt{a} + \sqrt{b}}, \frac{1}{\sqrt{a} + \sqrt{c}}, \frac{1}{\sqrt{b} + \sqrt{c}}$ are in

Five numbers are in $A.P.$,whose sum is $25$ and product is $2520$. If one of these five numbers is $-\frac{1}{2}$,then the greatest number amongst them is