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: 22


$\displaystyle s_1 =\dfrac{4}{3} \\s_2= \dfrac{16}{9} \\s_3= \dfrac{64}{27} \\s_4= \dfrac{256}{81} \\s_5=\dfrac{1024}{243}$

Work Step by Step

We are given that {$s_n$} $=\left(\dfrac{4}{3}\right)^n$ In order to determine the first five terms, we will have to substitute $n=1, 2,3,4,5$ into the given sequence {$s_n$}: $\displaystyle s_1 = (\dfrac{4}{3})^1=\dfrac{4}{3} \\s_2= (\dfrac{4}{3})^2=\dfrac{16}{9} \\s_3= (\dfrac{4}{3})^3=\dfrac{64}{27} \\s_4= (\dfrac{4}{3})^4=\dfrac{256}{81} \\s_5=(\dfrac{4}{3})^5=\dfrac{1024}{243}$
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