Chapter 11 - 11.3 - Geometric Sequences and Series - 11.3 Exercises - Page 795: 45

$a_6=-2$

$a_n=a_1r^{n-1}$ $a_4=a_1r^3$ $a_7=a_1r^6$ $\frac{a_7}{a_4}=\frac{a_1r^6}{a_1r^3}$ $\frac{\frac{2}{3}}{-18}=r^3$ $r^3=-\frac{1}{27}$ $r=\sqrt[3] {-\frac{1}{27}}=-\frac{1}{3}$ $\frac{a_7}{a_6}=r$ $a_6=\frac{a_7}{r}=\frac{\frac{2}{3}}{-\frac{1}{3}}=-2$