8. (i) A sequence of numbers is defined by
$$\begin{aligned}
u _ { 1 } & = 3
u _ { n + 1 } & = u _ { n } + 3 n - 2 \quad n \geqslant 1
\end{aligned}$$
Prove by induction that, for all positive integers \(n\),
$$u _ { n } = \frac { 3 } { 2 } n ^ { 2 } - \frac { 7 } { 2 } n + 5$$
(ii) Prove by induction that, for all positive integers \(n\),
$$f ( n ) = 3 ^ { 2 n + 3 } + 40 n - 27 \text { is divisible by } 64$$
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