Show that the sequence defined by $a_1=\frac{3}{2}$ and $a_{n1}=3-\frac{2}{a_n}$ is increasing and bounded above by $2.$ Deduce that $\{a_n\}$ converges and find its limit$.$

Show that the sequence defined by $a_1=\frac{3}{2}$ and $a_{n1}=\frac{2}{3-a_n}$ is decreasing and bounded below by $1.$ Deduce that $\{a_n\}$ converges and find its limit$.$