If the sum of $n$ terms of an $A.P.$ is $nA + n^2B$,where $A$ and $B$ are constants,then its common difference will be

Three positive numbers $a, b,$ and $c$ are in an Arithmetic Progression $(AP)$ and $abc = 4$. The minimum possible value of $b$ is:

If the roots of the equation $32x^3 - 48x^2 + 22x - 3 = 0$ are in arithmetic progression,then the square of the common difference of the roots is

If the $7^{th}$ term of an $A.P.$ is $40$,then the sum of the first $13$ terms is:

The sum of $24$ terms of the following series $\sqrt{2} + \sqrt{8} + \sqrt{18} + \sqrt{32} + \dots$ is

$150$ workers were engaged to finish a job in a certain number of days. $4$ workers dropped out on the second day,$4$ more workers dropped out on the third day,and so on. It took $8$ more days to finish the work. Find the number of days in which the work was completed.