Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 5 - Sequences, Mathematical Induction, and Recursion - Exercise Set 5.1: 7

Answer

First four terms of $a_k$ are 1, 3, 5, 7 First four terms of $b_k$ are 1, 3, 5, 13 First three terms match but fourth terms are different

Work Step by Step

$a_k = 2k+1$ $b_k = (k-1)^3 +k +2$ The first four terms of $a_k$ are $a_0 = 2(0)+1 = 1$ $a_1 = 2(1) + 1 = 3$ $a_2 = 2(2) + 1= 5$ $a_3 = 2(3) + 1 = 7$ The first four terms of $b_k$ are $b_0 = (0-1)^3 +0 +2 = 1$ $b_1 = (1-1)^3 +1 +2 = 3$ $b_2 = (2-1)^3 +2+2 = 5$ $b_3 = (3-1)^3 +3 +2 = 13$
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