Standard +0.3 This is a standard proof by induction with straightforward algebra. The base case is trivial (n=1 gives 8+27=35=7×5), and the inductive step requires only routine manipulation of powers and factoring out 7. While it's a 6-mark question requiring formal proof structure, it involves no conceptual difficulty beyond applying the standard induction template to a divisibility problem.
Prove by induction that, for $n \in \mathbb{Z}^+$
$$f(n) = 2^{n+2} + 3^{2n+1}$$
is divisible by 7
[6]
\hfill \mbox{\textit{SPS SPS FM Pure 2021 Q8 [6]}}