If $p(\frac{1}{q}+\frac{1}{r}), q(\frac{1}{r}+\frac{1}{p}), r(\frac{1}{p}+\frac{1}{q})$ are in $AP$,then $p, q, r$:

If the sum of $n$ terms of an $A.P.$ is $(pn + qn^2),$ where $p$ and $q$ are constants,find the common difference.

Let $x, y > 0$. If $x^{3} y^{2} = 2^{15}$,then the least value of $3x + 2y$ is

If all interior angles of a quadrilateral are in $A.P.$ and the common difference is $10^{\circ}$,find the smallest angle. (in $^{\circ}$)

If $\frac{3 + 5 + 7 + \dots \text{ to } n \text{ terms}}{5 + 8 + 11 + \dots \text{ to } 10 \text{ terms}} = 7$,then the value of $n$ is

Let $a_1, a_2, a_3, \ldots, a_{100}$ be an arithmetic progression with $a_1=3$ and $S_p=\sum_{i=1}^p a_i, 1 \leq p \leq 100$. For any integer $n$ with $1 \leq n \leq 20$,let $m=5n$. If $\frac{S_m}{S_n}$ does not depend on $n$,then $a_2$ is