The arithmetic progression (AP) is given by the sequence: 180, 175, 170, \ldots, 25.

The first term \(a = 180\) and the common difference \(d = 175 - 180 = -5\).

The last term \(l = 25\).

To find the number of terms \(n\), use the formula for the last term of an AP: \(l = a + (n-1) \cdot d\).

Substitute the known values: \(25 = 180 + (n-1) \cdot (-5)\).

Simplify: \(25 = 180 - 5(n-1)\).

\(25 = 180 - 5n + 5\).

\(25 = 185 - 5n\).

\(5n = 185 - 25\).

\(5n = 160\).

\(n = \frac{160}{5} = 32\).

Now, use the formula for the sum of an AP: \(S_n = \frac{n}{2} (a + l)\).

Substitute the known values: \(S_{32} = \frac{32}{2} (180 + 25)\).

\(S_{32} = 16 \cdot 205\).

\(S_{32} = 3280\).