Given the sum of the first \(n\) terms of an arithmetic progression: \(S_n = 32n - n^2\).

To find the first term \(a\), set \(n = 1\):

\(S_1 = 32(1) - 1^2 = 32 - 1 = 31\).

Thus, the first term \(a = 31\).

To find the common difference \(d\), set \(n = 2\):

\(S_2 = 32(2) - 2^2 = 64 - 4 = 60\).

The second term is given by \(S_2 - S_1 = 60 - 31 = 29\).

The common difference \(d = 29 - 31 = -2\).

Therefore, the first term is 31 and the common difference is -2.