If $a$,$b$,and $c$ are the first,second,and last terms of an arithmetic progression respectively,then the total number of terms is......

Let $S_{n}$ denote the sum of the first $n$ terms of an arithmetic progression. If $S_{10} = 530$ and $S_{5} = 140$,then $S_{20} - S_{6}$ is equal to:

The ratio of the sum of $m$ and $n$ terms of an $A.P.$ is $m^2:n^2$. Then the ratio of the $m^{th}$ and $n^{th}$ term will be:

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

Let $x_n, y_n, z_n, w_n$ denote the $n^{th}$ terms of four different arithmetic progressions with positive terms. If $x_4 + y_4 + z_4 + w_4 = 8$ and $x_{10} + y_{10} + z_{10} + w_{10} = 20$,then the maximum value of $x_{20} \cdot y_{20} \cdot z_{20} \cdot w_{20}$ is:

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