The \(1^{st}\) and \(8^{th}\) terms of an Arithmetic progression add up to \(32\), and multiplying them gives \(60\). Determine the values of the first term and the common difference. Then compute the sum of the first \(20\) terms of the sequence.
Answer:
The value of \(a=\) or
The value of \(a=\) or
The value of \(d=\) or
\(S_{20}=\) or
(Note: Enter the answers in ascending order).