8 Given the sequence $\left\{a_{n}\right\}$ satisfies $a_{1}=5, a_{n}=\frac{2 a_{n-1}-1}{a_{n-1}-2}\left(n \geqslant 2, n \in \mathbf{N}^{*}\right)$, then the sum of its first 100 terms is $\qquad$ .
8 Because $a_{1}=5$, then $a_{2}=3, a_{3}=5, a_{4}=3$, the sequence has a period of 2, so the sum of the first 100 terms is 400.