8-81 Let $a_{1}, a_{2}, \cdots$ and $b_{1}, b_{2}, \cdots$ be two arithmetic sequences, and their sums of the first $n$ terms are $A_{n}$ and $B_{n}$, respectively. It is known that for all $n \in N$,
$$
\frac{A_{n}}{B_{n}}=\frac{2 n-1}{3 n+1} .
$$

Try to write the expression for $\frac{a_{n}}{b_{n}}$ for all $n \in N$.