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 - Section 11.1 Sequences - 11.1 Assess Your Understanding - Page 827: 41

Answer

$a_2=\dfrac{3}{2} \\ a_3=\dfrac{1}{2} \\ a_4=\dfrac{1}{8} \\ a_5=\dfrac{1}{40} $

Work Step by Step

We are given that $a_n=\dfrac{a_{n-1}}{n}$ and $a_1= 3$. In order to determine the remaining values, we will have to substitute $n=2,3,4,5$ into the given sequence: $a_2=\dfrac{a_{1}}{2}=\dfrac{3}{2} \\ a_3=\dfrac{a_{2}}{3}=\dfrac{3/2}{2}=\dfrac{1}{2} \\ a_4=\dfrac{a_{3}}{4}=\dfrac{1/2}{4}=\dfrac{1}{8} \\ a_5=\dfrac{a_{4}}{5}=\dfrac{1/8}{5}=\dfrac{1}{40} $
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