## College Algebra 7th Edition

Published by Brooks Cole

# Chapter 8, Sequences and Series - Section 8.2 - Arithmetic Sequences - 8.2 Exercises: 24

#### Answer

There is a common difference of $\ln{2}$ therefore the given terms form an arithmetic sequence.

#### Work Step by Step

The given terms can be terms of an arithmetic sequence if there is a common difference among consecutive terms. First, simplify each expression using the rule $\ln{(a^n)}= n\cdot \ln{a}$. $\ln{2} = \ln{2}; \\\ln{4} = \ln{(2^2)}=2\ln{2}; \\\ln{8} = \ln{(2^3)}=3\ln{2}; \\\ln{16} = \ln{(2^4)} = 4\ln{2}$ Determine the difference between each pair of consecutive terms to obtain: $2\ln{2} - \ln{2} = \ln{2}; \\3\ln{2} - 2\ln{2} = \ln{2}; \\4\ln{2} - 3\ln{2} =\ln{2}$ There is a common difference of $\ln{2}$ therefore the given terms form an arithmetic sequence.

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