Problem

(a) The first, second and third terms of an arithmetic progression are $4k$, $k^2$ and $8k$ respectively, where $k$ is a non-zero constant.

(i) Find the value of $k$.

(ii) Find the sum of the first 20 terms of the progression.

(b) The fourth and sixth terms of a geometric progression are 36 and 6 respectively. The common ratio of the progression is positive.

Find the sum to infinity of the progression. Give your answer in the form $\frac{a}{\sqrt{b} - c}$, where $a$, $b$ and $c$ are integers.