4 The second term of a geometric progression is 24 . The sum to infinity of this progression is 150 . Write down two equations in \(a\) and \(r\), where \(a\) is the first term and \(r\) is the common ratio. Solve your equations to find the possible values of \(a\) and \(r\).
\(5 \quad S\) is the sum to infinity of a geometric progression with first term \(a\) and common ratio \(r\).

1. Another geometric progression has first term \(2 a\) and common ratio \(r\). Express the sum to infinity of this progression in terms of \(S\).
2. A third geometric progression has first term \(a\) and common ratio \(r ^ { 2 }\). Express, in its simplest form, the sum to infinity of this progression in terms of \(S\) and \(r\).