Chapter 11 - 11.3 - Geometric Sequences and Series - 11.3 Exercises - Page 795: 33

$a_n=128(\frac{1}{2})^n$

$a_1=64$ $r=\frac{a_2}{a_1}=\frac{a_3}{a_2}$ $r=\frac{32}{64}=\frac{16}{32}=\frac{1}{2}$ $a_n=a_1r^{n-1}$ $a_n=64(\frac{1}{2})^{n-1}=64(\frac{1}{2})^n(\frac{1}{2})^{-1}=64(\frac{1}{2})^n(2)=128(\frac{1}{2})^n$