8. Given the sequence $\left\{a_{n}\right\}$ satisfies
$$
a_{1}=5, a_{n}=\frac{2 a_{n-1}-1}{a_{n-1}-2}\left(n \geqslant 2, n \in \mathbf{N}_{+}\right) \text {. }
$$

Then the sum of its first 100 terms is $\qquad$
8.400.

Since $a_{1}=5$, then $a_{2}=3, a_{3}=5, a_{4}=3$, so the sequence has a period of 2. Therefore, the sum of the first 100 terms is 400.