College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 9 - Section 9.2 - Arithmetic Sequences - 9.2 Assess Your Understanding - Page 654: 15


common difference = $\ln{3}$ The first four terms are: $\ln{3}, 2\ln{3}, 3\ln{3}, 4\ln{3}$

Work Step by Step

To find the first four terms, substitute $1, 2, 3, 4$ for $n$ in the given formula; then, use the rule $\ln{(a^n)} = n\cdot\ln{a}$ to simplify. $s_1 = \ln{(3^1)} = \ln{3}$ $s_2= \ln{(3^2)}=2\cdot \ln{3}$ $s_3 = \ln{(3^3)} = 3 \cdot \ln{3}$ $s_4 = \ln{(3^4)}=4 \cdot \ln{3}$ The terms increase by $\ln{3}$ units, so the sequence is arithmetic with a common difference of $\ln{3}$.
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