(a)[5]
In an arithmetic progression, the total of the first ten terms is 400 and the total of the next ten terms is 1000. Determine the common difference and the first term.
(b)[5]
A geometric progression has first term $a$, common ratio $r$ and sum to infinity 6. Another geometric progression has first term $2a$, common ratio $r^2$ and sum to infinity 7. Find the values of $a$ and $r$.