Answer
$3n + 5$ is a even number if n is odd, because n can be write as $2k + 1$, substituting in the formula, we get 2(3k + 3) that is a even integer;
Work Step by Step
If $n$ is an odd integer. $n$ can be write as:
$n = 2 k + 1$
(with $k$ being one integer number)
$k \in \mathbb{Z}$
Now we can develop the formula $3n + 5$:
$\begin{split}
3n + 5 & = 3(2k + 1) + 5 \\
& = 6k + 1 + 5 \\
& = 6k + 6 \\
& = 2(3k + 3)
\end{split}$
Since $3k + 3k$ is an integer, then $2(3k + 3)$ is an even number, by the definition of even numbers.
