Chapter 8, Sequences and Series - Section 8.1 - Sequences and Summation Notation - 8.1 Exercises - Page 600: 8

$a_{1}=-\frac{1}{3}$ $a_{2}=\frac{1}{9}$ $a_{3}=-\frac{1}{27}$ $a_{4}=\frac{1}{81}$ $a_{100}=3^{-100}\approx 1.94\times 10^{-48}$

We are given: $a_{n}=( \frac{-1}{3})^{n}$ We evaluate: $a_{1}=(\frac{-1}{3})^{1}=-\frac{1}{3}$ $a_{2}=(\frac{-1}{3})^{2}=\frac{1}{9}$ $a_{3}=(\frac{-1}{3})^{3}=-\frac{1}{27}$ $a_{4}=(\frac{-1}{3})^{4}=\frac{1}{81}$ $a_{100}=(\frac{-1}{3})^{100}=3^{-100}\approx 1.94\times 10^{-48}$