College Algebra 7th Edition

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

Chapter 8, Sequences and Series - Section 8.3 - Geometric Sequences - 8.3 Exercises: 24

Answer

$a_1=7 \\a_2=13 \\a_3=31 \\a_4=85 \\a_5=247$ The sequence has no common ratio so it is not geometric.

Work Step by Step

To find the first five terms, substitute 1, 2, 3, 4, and 5 to the given formula to obtain: $a_1 = 4+3^1=4+3=7 \\a_2 = 4+3^2=4+19=13 \\a_3 = 4+3^3=4+27=31 \\a_4=4+3^4 = 4+81=85 \\a_5=4+3^5 = 4+243 = 247$ RECALL: A sequence is geometric if there is a common ratio among consecutive terms. The consecutive terms have no common ratio therefore the sequence is not geometric.
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