Prove by induction that $n(n+1)(n+5)$ is multiple of $3.$ $n(n+1)(n+5) = 3d$
I cannot figure out how to solve this homework question. A friend gave me a solution I couldn't make sense of, and I hope there's something easier out there. Also, what would be the general approach towards questions of this form?

Note that $n(n+1)(n+5) = n(n+1)(n+2+3) = n(n+1)(n+2) + 3n(n+1)$.
Now $n(n+1)(n+2)$ is always a multiple of $3$ and so is $n(n+1)(n+5)$, being a sum of two multiples of $3$.
