The sum of $n$ terms of an arithmetic progression is $nA + n^2B$,where $A$ and $B$ are constants. The common difference of this progression is.......

The condition that the roots of $x^3-b x^2+c x-d=0$ are in arithmetic progression is

If $a, b, c, d, e$ are in $A.P.$,then the value of $a + b + 4c - 4d + e$ in terms of $a$,if possible,is:

If $\log_3 2, \log_3(2^x - 5)$ and $\log_3(2^x - \frac{7}{2})$ are in $A.P.$,then $x$ is equal to

The sides of a right-angled triangle are in arithmetic progression. If the triangle has an area of $24$,then what is the length of its smallest side?

Consider an $A$.$P$.: $a_1, a_2, \dots, a_n$, with $a_1 > 0$. If $a_2 - a_1 = -\frac{3}{4}$, $a_n = \frac{1}{4} a_1$, and $\sum_{i=1}^n a_i = \frac{525}{2}$, then $\sum_{i=1}^{17} a_i$ is equal to: