The sixth term of an arithmetic progression is 23 and the sum of the first ten terms is 200 . Find the seventh term.
A geometric progression has first term 1 and common ratio \(r\). A second geometric progression has first term 4 and common ratio \(\frac { 1 } { 4 } r\). The two progressions have the same sum to infinity, \(S\). Find the values of \(r\) and \(S\).