The ratio of the sums of the first $n$ even numbers and $n$ odd numbers is:

If the $n^{th}$ term of an arithmetic progression is $3n - 1$,then the sum of its first five terms is.......

Let the six numbers $a_1, a_2, a_3, a_4, a_5, a_6$ be in $A.P.$ and $a_1+a_3=10$. If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^2$,then $8 \sigma^2$ is equal to

If $x, y, z$ are three real numbers with the same sign,then the value of $\frac{x}{y} + \frac{y}{z} + \frac{z}{x}$ lies in which interval?

If the $m^{th}$ term of an arithmetic progression is $1/n$ and the $n^{th}$ term is $1/m$,then the sum of the first $mn$ terms is:

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 $\frac{S_1}{n_1}(n_2 - n_3) + \frac{S_2}{n_2}(n_3 - n_1) + \frac{S_3}{n_3}(n_1 - n_2) = ....$