7.
$$f ( n ) = 2 ^ { n } + 6 ^ { n }$$
- Show that \(\mathrm { f } ( k + 1 ) = 6 \mathrm { f } ( k ) - 4 \left( 2 ^ { k } \right)\).
- Hence, or otherwise, prove by induction that, for \(n \in \mathbb { Z } ^ { + } , \mathrm { f } ( n )\) is divisible by 8 .