The sums of $n$ terms of two arithmetic series are in the ratio $(2n + 3) : (6n + 5)$. Then the ratio of their $13^{th}$ terms is:

In an arithmetic progression,if $T_m = n$ and $T_n = m$,then $T_p = \dots$

Let $a_1=8, a_2, a_3, \ldots, a_n$ be an $A.P.$ If the sum of its first four terms is $50$ and the sum of its last four terms is $170$,then the product of its middle two terms is

Consider two sets $A$ and $B$,each containing three numbers in $A.P.$ Let the sum and the product of the elements of $A$ be $36$ and $p$ respectively,and the sum and the product of the elements of $B$ be $36$ and $q$ respectively. Let $d$ and $D$ be the common differences of the $A.P.s$ in $A$ and $B$ respectively such that $D = d + 3$ and $d > 0$. If $\frac{p + q}{p - q} = \frac{19}{5}$,then $p - q$ is equal to:

If the sum of three numbers in an arithmetic progression is $33$ and their product is $792$,what is the smallest number among them?

If for an arithmetic progression $S_{2n} = 2S_n$,then $S_{3n} / S_n = \dots$