If the $p^{th}$ term of an arithmetic progression is $q$ and the $q^{th}$ term is $p$,then its $r^{th}$ term is:

Suppose that the number of terms in an $A.P.$ is $2k$,where $k \in N$. If the sum of all odd-positioned terms of the $A.P.$ is $40$,the sum of all even-positioned terms is $55$,and the last term of the $A.P.$ exceeds the first term by $27$,then $k$ is equal to:

If the middle term of the $AP$ is $300$,then the sum of its first $51$ terms is

Let $S_n$ denote the sum of $n$ terms of an $A.P.$ If $S_{2n} = 3S_n$,then the ratio $\frac{S_{3n}}{S_n} = $

The sum of $1 + 3 + 5 + 7 + \dots$ up to $n$ terms is

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: