9. (i) A sequence of numbers is defined by $$\begin{gathered} u _ { 1 } = 6 , \quad u _ { 2 } = 27
u _ { n + 2 } = 6 u _ { n + 1 } - 9 u _ { n } \quad n \geqslant 1 \end{gathered}$$ Prove by induction that, for \(n \in \mathbb { Z } ^ { + }\) $$u _ { n } = 3 ^ { n } ( n + 1 )$$ (ii) Prove by induction that, for \(n \in \mathbb { Z } ^ { + }\) $$f ( n ) = 3 ^ { 3 n - 2 } + 2 ^ { 3 n + 1 } \text { is divisible by } 19$$ \includegraphics[max width=\textwidth, alt={}, center]{536d7ec7-91b0-4fda-a485-2ac4a72c7d59-29_56_20_109_1950}