(a)[3]
For an arithmetic progression with the sum of the first $n$ terms, $S_n$, given by $S_n = n^2 + 8n$, determine the first term and the common difference.
(b)[5]
In a geometric progression, the second term is $9$ less than the first term. The total of the second and third terms is $30$. If every term in the progression is positive, find the first term.