Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 8 - Sequences and Infinite Series - 8.1 An Overview - 8.1 Exercises: 55

Answer

a) $\{10,5,2.5,1.25\}$ b) $h_n = 0.5^n(20)$

Work Step by Step

a) $h_0 = 20$; $h_n = r(h_{n-1})$ $h_n = 0.5h_{n-1}$ $h_1 = 0.5h_0 = 10$ $h_2 = 0.5h_1 = 5$ $h_3 = 0.5h_2 = 2.5$ $h_4 = 0.5h_3 = 1.25$ b) We need to multiply by a factor of $r$ a total of $n$ times to the original value of $h_0$. $h_n = r^nh_0 = 0.5^n(20)$
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