The first, second and third terms of an arithmetic progression are \(a\), \(\frac{3}{2}a\) and \(b\) respectively, where \(a\) and \(b\) are positive constants. The first, second and third terms of a geometric progression are \(a\), 18 and \(b + 3\) respectively.

(a) Find the values of \(a\) and \(b\).

(b) Find the sum of the first 20 terms of the arithmetic progression.