The first three terms of a geometric progression are positive constants \(a,b,c\). The first three terms of an arithmetic progression are \(a,b,-3c\).

(a) Show \(a^2-10ac+9c^2=0\). [3]

Now \(a=9\), and \(c\) takes its smaller possible value.

(b)(i) Find the geometric progression’s sum to infinity. [5]

(b)(ii) Find the sum of the first 20 terms of the arithmetic progression. [3]