College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.2 - Arithmetic Sequences - 8.2 Exercises: 32

Answer

The first five terms are: $a_1 = 2$ $a_2 = 4$ $a_3 = 2$ $a_4 = 4$ $a_5 = 2$ The terms do not have a common difference so the sequence is not arithmetic.

Work Step by Step

Find the first five terms by substituting 1, 2, 3, 4 and 5 to $n$ in the given formula. $a_1 = 3+(-1)^1(1) = 3+(-1)(1) = 3+(-1) = 2$ $a_2 = 3+(-1)^2(1) = 3+(1) = 3+1 = 4$ $a_3 = 3+(-1)^3(1) = 3+(-1)(1) = 3+(-1) = 2$ $a_4 = 3+(-1)^4(1) = 3+1(1) = 3+1 = 4$ $a_5 = 3+(-1)^5(1) = 3+(-1)(1) = 3+(-1) = 2$ A sequence is arithmetic if there exists a common difference among consecutive terms. The terms do not have a common difference. Thus, the sequence is not arithmetic.
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