6. Given the sequence $\left\{a_{n}\right\}$ with the general term $a_{n}=\left(\frac{2}{3}\right)^{n-1}\left[\left(\frac{2}{3}\right)^{n-1}-1\right]$. Which of the following statements is correct? (A) The maximum term is $a_{1}$, the minimum term is $a_{4}$ (B) The maximum term is $a_{1}$, the minimum term does not exist (C) The maximum term does not exist, the minimum term is $a_{3}$ (D) The maximum term is $a_{1}$, the minimum term is $a_{3}$
6.D.
$$
a_{1}=0, a_{2}=-\frac{2}{9}, a_{3}=-\frac{20}{81} \text {. }
$$

When $n>3$, $t=\left(\frac{2}{3}\right)^{n-1}$ is a decreasing function, and
$$
0>a_{n}>a_{n-1}>\cdots>a_{4}>a_{3}$.
Therefore, $a_{1}$ is the largest, and $a_{3}$ is the smallest.