(a)[4]
An arithmetic progression has sixth term $23$ and total of the first ten terms $200$. Determine the seventh term.
(b)[3]
A geometric progression starts with first term $1$ and has common ratio $r$. A second geometric progression starts with first term $4$ and has common ratio $\frac{1}{4}r$. Both progressions share the same sum to infinity, $S$. Determine $r$ and $S$.