If $x, 2 y$ and $3 z$ are in AP where the distinct numbers $x, y$ and $z$ are in GP, then the common ratio of the GP is

If in an $A P, S_n=q n^2$ and $S_m=q m^2$, where $S_r$ denotes the sum of $r$ terms of the $A P$, then $S_q$ equals to

Let $S_n$ denote the sum of the first $n$ terms of an AP, if $S_{2 n}=3 S_n$, then $S_{3 n}: S_n$ is equal to

The minimum value of $4^x+4^{1-x}, x \in R$ is

Let $S_n$ denote the sum of the cubes of the first $n$ natural numbers and $s_n$ denote the sum of the first $n$ natural numbers, then $\sum_\limits{r=1}^n \frac{S_r}{S_4}$ equals to