Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 11 - Sequences; Induction; the Binomial Theorem - Chapter Review - Review Exercises - Page 859: 3

Answer

$a_1=3 \\ a_2=2 \\ a_3=\dfrac{4}{3} \\a_4=\dfrac{8}{9} \\a_5=\dfrac{16}{27}$

Work Step by Step

We are given: $\{a_n\}=\dfrac{2}{3}a_{n-1}$ and $a_1=3$ In order to determine the remaining values, we will have to substitute $n=1, 2,3,4,5$ into the given sequence. $a_2=\dfrac{2}{3}a_1=\dfrac{2}{3}3=2 \\ a_3=\dfrac{2}{3}a_2=\dfrac{2}{3}2=\dfrac{4}{3} \\a_4=\dfrac{2}{3}a_3=\dfrac{2}{3} \cdot \dfrac{4}{3}=\dfrac{8}{9} \\a_5=\dfrac{2}{3} a_4=\dfrac{2}{3} \cdot \dfrac{8}{9}=\dfrac{16}{27}$
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.