6. If the infinite decreasing geometric sequence $\left\{a_{n}\right\}$ satisfies $\lim _{n \rightarrow \infty} \frac{a_{1}+a_{4}+a_{7}+\cdots+a_{3 n-2}}{a_{1}+a_{2}+\cdots+a_{n}}=\frac{3}{4}$, then the common ratio of the sequence is ( ).
A. $\frac{\sqrt{21}-3}{6}$
B. $\frac{-3-\sqrt{21}}{6}$
C. $\frac{\sqrt{21} \pm 3}{6}$
D. $\frac{-3 \pm \sqrt{21}}{6}$
6. A. $\lim _{n \rightarrow \infty} \frac{a_{1}+a_{4}+\cdots+a_{3 n-2}}{a_{1}+a_{2}+\cdots+a_{n}}=\frac{a_{1}}{1-q^{3}} \cdot \frac{1-q}{a_{1}}=\frac{1}{q^{2}+q+1}=\frac{3}{4}$, so $q=\frac{\sqrt{21}-3}{6}$.