6. Given the sequence: $\frac{2}{3}, \frac{2}{9}, \frac{4}{9}, \frac{6}{9}, \frac{8}{9}, \frac{2}{27}, \frac{4}{27}, \cdots$, $\frac{26}{27}, \cdots, \frac{2}{3^{n}}, \frac{4}{3^{n}}, \cdots, \frac{3^{n}-1}{3^{n}}, \cdots$. Then $\frac{2018}{2187}$ is the $\qquad$th term of the sequence.
6. 1552 .

Upon observation, $\frac{2018}{2187}$ is the
$$
\frac{3-1}{2}+\frac{3^{2}-1}{2}+\cdots+\frac{3^{6}-1}{2}+\frac{2018}{2}
$$

term. Using a TI calculator, it is calculated that $\frac{2018}{2187}$ is the 1552nd term.