2 It is given that \(\mathrm { f } ( n ) = 2 ^ { 3 n } + 8 ^ { n - 1 }\). By simplifying \(\mathrm { f } ( k ) + \mathrm { f } ( k + 1 )\), or otherwise, prove by mathematical induction that \(\mathrm { f } ( n )\) is divisible by 9 for every positive integer \(n\).
2 It is given that $\mathrm { f } ( n ) = 2 ^ { 3 n } + 8 ^ { n - 1 }$. By simplifying $\mathrm { f } ( k ) + \mathrm { f } ( k + 1 )$, or otherwise, prove by mathematical induction that $\mathrm { f } ( n )$ is divisible by 9 for every positive integer $n$.\\
\hfill \mbox{\textit{CAIE FP1 2018 Q2}}