Answer
Monotonic and Unbounded (not bounded from above)
Work Step by Step
$a_{n+1}\:=\:\left(\frac{3}{2}\right)^{n+1}\:=\:\frac{3}{2}\:\times \:\left(\frac{3}{2}\right)^n\:=\:\:\frac{3}{2}\:\times \:a_n\:>\:a_n$
Implies $a_{n+1}\:>\:a_n$
Therefore the sequence is strictly decreasing and hence monotonic.
There is no number x such that $\left(\frac{3}{2}\right)^n$ is less than x for all n. This is because $\frac{3}{2}>1$ and hence its powers increase without bounds. Thus it is unbounded from above.
