(i) For the arithmetic progression, the first term is \(a = 12\) and the fifth term is \(a + 4d = 18\). Solving for \(d\), we have:

\(a + 4d = 18\)

\(12 + 4d = 18\)

\(4d = 6\)

\(d = 1.5\)

The sum of the first 25 terms \(S_{25}\) is given by:

\(S_{25} = \frac{25}{2} (2a + (25-1)d)\)

\(S_{25} = \frac{25}{2} (24 + 24 \times 1.5)\)

\(S_{25} = 750\)

(ii) For the geometric progression, the first term is \(a = 12\) and the fifth term is \(ar^4 = 18\). Solving for \(r\), we have:

\(ar^4 = 18\)

\(12r^4 = 18\)

\(r^4 = 1.5\)

The 13th term \(ar^{12}\) is given by:

\(ar^{12} = 12 \times (1.5)^3\)

\(ar^{12} = 40.5 \text{ or } 40.6\)