Chapter 11 - 11.3 - Geometric Sequences and Series - 11.3 Exercises - Page 795: 34

$a_n=243(\frac{1}{3})^n$

$a_1=81$ $r=\frac{a_2}{a_1}=\frac{a_3}{a_2}$ $r=\frac{27}{81}=\frac{9}{27}=\frac{1}{3}$ $a_n=a_1r^{n-1}$ $a_n=81(\frac{1}{3})^{n-1}=81(\frac{1}{3})^n(\frac{1}{3})^{-1}=81(\frac{1}{2})^n(3)=243(\frac{1}{3})^n$