College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.1 - Sequences and Summation Notation - 8.1 Exercises: 30

Answer

$a_{n}=\frac{(-1)^{n}}{3^{n}}$

Work Step by Step

We are given: $-\frac{1}{3}, \frac{1}{9}, - \frac{1}{27}, \frac{1}{81}$, ... We notice that there are powers of 3 in the denominator. In addition, the signs of the terms alternate. We find the pattern: $a_{1}=\frac{(-1)^{1}}{3^{1}}$ $a_{2}=\frac{(-1)^{2}}{3^{2}}$ $a_{3}=\frac{(-1)^{3}}{3^{3}}$ $a_{4}=\frac{(-1)^{4}}{3^{4}}$ ... $a_{n}=\frac{(-1)^{n}}{3^{n}}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.