let $(a\_1,\cdots,a\_n)$ be a list of integers prove that if $a\_1$ is even and $a\_n$ is odd then there is an index $i$, $1\leq i < n$ such that $a\_i$ is even and $a\_i+1$ is odd. I’m extremely confused on how to even preform induction on this. What would the base case even be?