9. (i) A sequence of numbers is defined by $$\begin{gathered} u _ { 1 } = 0 \quad u _ { 2 } = - 6
u _ { n + 2 } = 5 u _ { n + 1 } - 6 u _ { n } \quad n \geqslant 1 \end{gathered}$$ Prove by induction that, for \(n \in \mathbb { Z } ^ { + }\) $$u _ { n } = 3 \times 2 ^ { n } - 2 \times 3 ^ { n }$$ (ii) Prove by induction that, for all positive integers \(n\), $$f ( n ) = 3 ^ { 3 n - 2 } + 2 ^ { 4 n - 1 }$$ is divisible by 11