Answer
$a_n$ is bounded and decreasing.
Work Step by Step
The derivative of the corresponding function $f(x)= \frac{1- x}{2+x}$ with respects to x is $f'(x)= \frac{-3}{(x+2)^2} $. Since the derivative is always negative, $a_n$ is decreasing.
$\lim\limits_{n \to \infty}\frac{1- n}{2+n}= \lim\limits_{n \to \infty}\frac{\frac{1}{n}-1}{\frac{2}{n}+1}= -1=\lim\limits_{n \to -\infty}\frac{1- n}{2+n}$
$a_n$ is bounded from above and from below by -1. The sequence is bounded.
