1. The $n$th term for the sequence of even numbers, $P$, is $2n$.

The $n$th term for the sequence of odd numbers, $Q$, is $2n-1$.

A new sequence $R$ is formed using the two sequences. Each term of $R$ is calculated by squaring the corresponding term of $P$ and then subtracting the corresponding term of $Q$.

Show that all the terms in the sequence $R$ are odd.