Let the sum of the first $n$ terms of a non-constant $A.P., a_1, a_2, a_3, ……$ be $50\,n\, + \,\frac{{n\,(n\, - 7)}}{2}A,$ where $A$ is a constant. If $d$ is the common difference of this $A.P.,$ then the ordered pair $(d,a_{50})$ is equal to

The first term of an $A.P. $ is $2$ and common difference is $4$. The sum of its $40$ terms will be

For three positive integers $p , q , r , x ^{ pq p ^2}= y ^{ qr }= z ^{ p ^2 r }$ and $r=p q+1$ such that $3,3 \log _y x, 3 \log _z y, 7 \log _x z$ are in A.P. with common difference $\frac{1}{2}$. Then $r - p - q$ is equal to

If the ${p^{th}}$ term of an $A.P.$ be $\frac{1}{q}$ and ${q^{th}}$ term be $\frac{1}{p}$, then the sum of its $p{q^{th}}$ terms will be

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

The sum of the series $\frac{1}{2} + \frac{1}{3} + \frac{1}{6} + ........$ to $9$ terms is