In an arithmetic progression the sum of the first ten terms is 400 and the sum of the next ten terms is 1000 . Find the common difference and the first term.
A geometric progression has first term \(a\), common ratio \(r\) and sum to infinity 6. A second geometric progression has first term \(2 a\), common ratio \(r ^ { 2 }\) and sum to infinity 7 . Find the values of \(a\) and \(r\).