Chapter 11 - 11.3 - Geometric Sequences and Series - 11.3 Exercises - Page 795: 42

$a_8=\frac{64}{729}$

$a_1=\frac{3}{2}$ $r=\frac{a_2}{a_1}=\frac{a_3}{a_2}$ $r=\frac{-1}{\frac{3}{2}}=\frac{\frac{2}{3}}{-1}=-\frac{2}{3}$ $a_n=a_1r^{n-1}$ $a_8=\frac{3}{2}(-\frac{2}{3})^{8-1}=\frac{3}{2}(-\frac{2}{3})^7=(\frac{2}{3})^{-1}(-\frac{2}{3})^7=(-\frac{2}{3})^6=\frac{64}{729}$