(i) Start with \(x_1 = 3.5\).

Calculate \(x_2 = \frac{3.5(3.5^3 + 100)}{2(3.5^3 + 25)} = 3.683943\).

Calculate \(x_3 = \frac{3.683943(3.683943^3 + 100)}{2(3.683943^3 + 25)} = 3.684002\).

Calculate \(x_4 = \frac{3.684002(3.684002^3 + 100)}{2(3.684002^3 + 25)} = 3.684000\).

Calculate \(x_5 = \frac{3.684000(3.684000^3 + 100)}{2(3.684000^3 + 25)} = 3.684000\).

The sequence converges to \(\alpha = 3.6840\) correct to 4 decimal places.

(ii) The equation satisfied by \(\alpha\) is \(x = \frac{x(x^3 + 100)}{2(x^3 + 25)}\).

Solving for \(x\), we find \(\alpha = 3\sqrt{50}\).