a) The sixth term of an arithmetic progression is 23 and the sum of the first ten terms is 200. Find the seventh term.
b) 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 $S$.
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