(a)[3]
In an arithmetic progression, the sum $S_n$ of the first $n$ terms is $S_n = 2n^2 + 8n$. Determine the first term and the common difference of the progression.
(b)[5]
The first $2$ terms of a geometric progression are $64$ and $48$ respectively. Those same first $3$ terms of the geometric progression are, respectively, the $1$st term, the $9$th term and the $n$th term of an arithmetic progression. Find the value of $n$.