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

If the sum of the series $54 + 51 + 48 + \dots$ is $513$,then the number of terms is:

The sum of $n$ arithmetic means between $a$ and $b$ is:

Let $S_{1}$ be the sum of the first $2n$ terms of an arithmetic progression. Let $S_{2}$ be the sum of the first $4n$ terms of the same arithmetic progression. If $(S_{2} - S_{1})$ is $1000$,then the sum of the first $6n$ terms of the arithmetic progression is equal to:

If the roots of the equation $4x^3 - 12x^2 + 11x + m = 0$ are in arithmetic progression,then $m =$

If $\frac{1}{b - c}, \frac{1}{c - a}, \frac{1}{a - b}$ are consecutive terms of an $A.P.$,then $(b - c)^2, (c - a)^2, (a - b)^2$ will be in