The arithmetic mean of the first $n$ even natural numbers 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

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

If the sum of first $n$ terms of an $A.P.$ is equal to the sum of its first $m$ terms,$(m \ne n)$,then the sum of its first $(m + n)$ terms will be

If the sum of two extreme numbers of an $A.P.$ with four terms is $8$ and the product of the remaining two middle terms is $15$,then the greatest number of the series will be:

If $p$ times the $p^{th}$ term of an arithmetic progression is equal to $q$ times its $q^{th}$ term,then the $(p + q)^{th}$ term of this progression is........