9 A geometric progression has first term \(a\) and common ratio \(r\), and the terms are all different. The first, second and fourth terms of the geometric progression form the first three terms of an arithmetic progression.
- Show that \(r ^ { 3 } - 2 r + 1 = 0\).
- Given that the geometric progression converges, find the exact value of \(r\).
- Given also that the sum to infinity of this geometric progression is \(3 + \sqrt { 5 }\), find the value of the integer \(a\).