6 From the problem, we have $a_{1}=0, a_{2}=-\frac{2}{9}, a_{3}=-\frac{20}{81}$. When $n \geqslant 3$, $t=\left(\frac{2}{3}\right)^{n-1}$ is a decreasing function, and
$$
0a_{n}>a_{n-1}>\cdots>a_{4}>a_{3} .
$$

Therefore, $a_{1}$ is the largest, and $a_{3}$ is the smallest. Hence, the answer is D.
(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 $a_{3}$