(i) From the arithmetic progression (AP), we have:

\(x - 4 = y - x\)

From the geometric progression (GP), we have:

\(\frac{y}{x} = \frac{18}{y}\)

Solving the GP equation gives:

\(y^2 = 18x\)

Substitute \(x = \frac{y^2}{18}\) into the AP equation:

\(\frac{y^2}{18} - 4 = y - \frac{y^2}{18}\)

Rearrange and simplify:

\(4 + 2\left(\frac{y^2}{18} - 4\right) = y\)

\(y^2 - 9y - 36 = 0\)

Solving this quadratic equation gives:

\(x = 8, y = 12\)

(ii) For the AP, the fourth term is:

\(4 + 3d = 16\)

For the GP, the fourth term is:

\(8 \times \left(\frac{12}{8}\right)^3 = 27\)