(i) For the geometric progression (GP), the terms are \(8, 8r, 8r^2\).

For the arithmetic progression (AP), the terms are \(8, 8 + 8d, 8 + 20d\).

Equating the terms: \(8r = 8 + 8d\) and \(8r^2 = 8 + 20d\).

From \(8r = 8 + 8d\), we get \(r = 1 + d\).

Substitute \(d = r - 1\) into \(8r^2 = 8 + 20d\):

\(8r^2 = 8 + 20(r - 1)\)

\(8r^2 = 8 + 20r - 20\)

\(8r^2 = 20r - 12\)

\(8r^2 - 20r + 12 = 0\)

Divide by 4: \(2r^2 - 5r + 3 = 0\)

Solving the quadratic: \((2r - 3)(r - 1) = 0\)

\(r = 1.5\) (since \(r \neq 1\))

(ii) The 4th term of the GP is \(ar^3 = 8 \times (1.5)^3 = 27\).

For the AP, \(d = 0.5\) (since \(r = 1.5\) and \(r = 1 + d\)).

The 4th term of the AP is \(a + 3d = 8 + 3 \times 0.5 = 9.5\).