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: 28

Answer

The first five terms are: $a_1 = 6$ $a_2 = 8$ $a_3 = 12$ $a_4 = 20$ $a_5 = 36$ The sequence has no common difference so it 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. $a_1 = 4+2^1=4+2=6$ $a_2 = 4+2^2=4+4=8$ $a_3 = 4+2^3=4+8=12$ $a_4 = 4+2^4 = 4+16=20$ $a_5 = 4+2^5 = 4+32=36$ A sequence is arithmetic if there exists common difference among consecutive terms. The sequence has no common difference so it is not arithmetic.
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