8 A geometric progression has first term \(a\), common ratio \(r\) and sum to infinity \(S\). A second geometric progression has first term \(a\), common ratio \(R\) and sum to infinity \(2 S\).
- Show that \(r = 2 R - 1\).
It is now given that the 3rd term of the first progression is equal to the 2nd term of the second progression. - Express \(S\) in terms of \(a\).