There are $n$ arithmetic means between $7$ and $71$. If the $5^{th}$ arithmetic mean is $27$,then $n = ......$

Let $a_{1}, a_{2}, \ldots, a_{21}$ be an $A.P.$ such that $\sum_{n=1}^{20} \frac{1}{a_{n} a_{n+1}} = \frac{4}{9}$. If the sum of this $A.P.$ is $189$,then $a_{6} a_{16}$ is equal to:

If $a_m$ denotes the $m^{th}$ term of an $A.P.$,then $a_m$ =

Let $S_{n}$ be the sum of the first $n$ terms of an arithmetic progression. If $S_{3n} = 3S_{2n}$,then the value of $\frac{S_{4n}}{S_{2n}}$ is:

The condition that the roots of $x^3-b x^2+c x-d=0$ are in arithmetic progression is

If the sum of $n$ terms of an arithmetic progression is given by $Pn + Qn^2$,where $P$ and $Q$ are constants,what is the common difference?