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

If $t_n$ denotes the $n$th term of the series $2+3+6+11+18+\ldots$, then $t_{50}$ is

The lengths of three unequal edges of a rectangular solid block are in GP. If the volume of the block is $216 \mathrm{~cm}^3$ and the total surface area is $252 \mathrm{~cm}^2$, then the length of the longest edge is