Bounding a Recursive Term

In a sequence $\{a_n\}$, $a_1=3$ and $a_{n+1}a_n+\lambda a_{n+1}+\mu a_n^2=0$ for $n\in\mathbb N^{*}$.

1. If $\lambda=0$ and $\mu=-2$, find the general term of $\{a_n\}$. 2. If $\lambda=\dfrac 1{k_0}$ (where $k_0\in\mathbb N^{*}$, $k_0\geqslant 2$) and $\mu=-1$, prove that