A geometric progression has first term \(a ( a \neq 0 )\), common ratio \(r\) and sum to infinity \(S\). A second geometric progression has first term \(a\), common ratio \(2 r\) and sum to infinity \(3 S\). Find the value of \(r\).
An arithmetic progression has first term 7. The \(n\)th term is 84 and the ( \(3 n\) )th term is 245 . Find the value of \(n\).