In an arithmetic progression, the sum, \(S _ { n }\), of the first \(n\) terms is given by \(S _ { n } = 2 n ^ { 2 } + 8 n\). Find the first term and the common difference of the progression.
The first 2 terms of a geometric progression are 64 and 48 respectively. The first 3 terms of the geometric progression are also the 1st term, the 9th term and the \(n\)th term respectively of an arithmetic progression. Find the value of \(n\).