Let $S_{n}$ be the sum of the first $n$ terms of an arithmetic progression. If $S_{3n} = 3S_{2n}$,then the value of $\frac{S_{4n}}{S_{2n}}$ is:

The ratio of the sum of $m$ and $n$ terms of an $A.P.$ is $m^2:n^2$. Then the ratio of the $m^{th}$ and $n^{th}$ term will be:

If $S_1, S_2$ and $S_3$ are the sums of the first $n_1, n_2$ and $n_3$ terms of an arithmetic progression respectively,then $\frac{S_1}{n_1}(n_2 - n_3) + \frac{S_2}{n_2}(n_3 - n_1) + \frac{S_3}{n_3}(n_1 - n_2) = ....$

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of an arithmetic progression are $1/a$,$1/b$,and $1/c$ respectively,then $ab(p - q) + bc(q - r) + ca(r - p) = \dots$

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

There are $15$ terms in an arithmetic progression. Its first term is $5$ and their sum is $390$. The middle term is