Example 1. The unit digit sequence formed by 2: 2, $4,8,6,2,4,8,6, \cdots$, try to find the general term formula of this sequence.
The essence of the problem is to find the general term formula of the sequence $\left\{a_{\mathrm{n}}\right\}$, where $D_{n+4}=a_{n}$, and $a_{1}=2, a_{2}=4, a_{3}=8, a_{4}=6$.

Since the characteristic equation of this sequence is $\lambda^{4}-1=0$, the characteristic roots are $\lambda_{1}=1, \lambda_{2}=-1, \lambda_{3}=\cos \frac{\pi}{2} + i \sin \frac{\pi}{2}, \lambda_{4}=\cos \frac{\pi}{2} - i \sin \frac{\pi}{2}$. Therefore, we can assume the general term formula of this sequence to be:
$$
a_{\mathrm{n}}=c_{1}+(-1)^{n} c_{2}+A \cos \frac{n \pi}{2}+B \sin \frac{n \pi}{2} .
$$