If the roots of the equation ${x^3} - 12{x^2} + 39x - 28 = 0$ are in $A.P.$,then their common difference will be

The geometric and harmonic means of two numbers $x_1$ and $x_2$ are $18$ and $16\frac{8}{13}$ respectively. The value of $|x_1 - x_2|$ is

Let $\frac{1}{x_1}, \frac{1}{x_2}, \frac{1}{x_3}, \dots, \frac{1}{x_n}$ ($x_i \neq 0$ for $i = 1, 2, \dots, n$) be in $A.P.$ such that $x_1 = 4$ and $x_{21} = 20$. If $n$ is the least positive integer for which $x_n > 50$,then $\sum_{i=1}^n \frac{1}{x_i}$ is equal to:

Sum of the $n$ terms of the series $\frac{3}{1^2} + \frac{5}{1^2 + 2^2} + \frac{7}{1^2 + 2^2 + 3^2} + ...$ is

Let $S_n$ denote the sum of the first $n$ terms of an $A.P$. If $S_4 = 16$ and $S_6 = -48$,then $S_{10}$ is equal to

If twice the $11^{th}$ term of an $A.P.$ is equal to $7$ times of its $21^{st}$ term,then its $25^{th}$ term is equal to