Answer
Increasing and bounded.
Work Step by Step
The function $f(x)= 3- 2x e^{-x}$ is always increasing for all $x\geq 1$. Therefore, the corresponding sequence $a_n= 3- 2n e^{-n}$ is increasing.
$\lim\limits_{n \to \infty}= 3- 2 \lim\limits_{n \to \infty}= 3- 2*0= 3$
The sequence has 3 as an upper bound. Thus, since all increasing sequences are bounded below , $a_n$ is bounded.
