The sum of $n$ arithmetic means between $a$ and $b$, is

If $a_m$ denotes the mth term of an $A.P.$ then $a_m$ =

Let $a_{1}, a_{2}, \ldots \ldots, a_{21}$ 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 AP is $189,$ then  $a_{6} \mathrm{a}_{16}$ is equal to :

If $p$ times the ${p^{th}}$ term of an $A.P.$ is equal to $q$ times the ${q^{th}}$ term of an $A.P.$, then ${(p + q)^{th}}$ term is

The four arithmetic means between $3$ and $23$ are

The number of terms common to the two A.P.'s $3,7,11, \ldots ., 407$ and $2,9,16, \ldots . .709$ is