If $p(\frac{1}{q}+\frac{1}{r}), q(\frac{1}{r}+\frac{1}{p}), r(\frac{1}{p}+\frac{1}{q})$ are in $AP$,then $p, q, r$:

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:

The $n^{th}$ term of an $A.P.$ is $3n - 1$. Choose from the following the sum of its first five terms.

Find the mean of the first $n$ terms of the $A$.$P$. $a, (a + d), (a + 2d), \dots$

Which term of the sequence $(-8 + 18i), (-6 + 15i), (-4 + 12i), \dots$ is purely imaginary (in $^{th}$)?

Statement-$I$: If the ratio of the sum of $n$ terms of two arithmetic progressions is $(7n + 1) : (4n + 17)$,then the ratio of their $n^{th}$ terms is $7 : 4$.
Statement-$II$: If $S_n = an^2 + bn + c$,then $T_n = S_n - S_{n-1}$.