(i) For an arithmetic progression, the first term is \(a = 4\) and the common difference \(d = 8 - 4 = 4\). The sum of the first \(n\) terms is given by:

\(S_n = \frac{n}{2} (2a + (n-1)d)\)

Substituting \(n = 10\), \(a = 4\), and \(d = 4\):

\(S_{10} = \frac{10}{2} (2 \times 4 + 9 \times 4) = 5 (8 + 36) = 5 \times 44 = 220\)

(ii) For a geometric progression, the first term is \(a = 4\) and the common ratio \(r = \frac{8}{4} = 2\). The sum of the first \(n\) terms is given by:

\(S_n = a \frac{r^n - 1}{r - 1}\)

Substituting \(n = 10\), \(a = 4\), and \(r = 2\):

\(S_{10} = 4 \frac{2^{10} - 1}{2 - 1} = 4 (1024 - 1) = 4 \times 1023 = 4092\)