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: 26

Answer

There is no common difference so the given terms cannot be terms of 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. Determine the difference between each pair of consecutive terms. Make the fractions similar sing their LCD. $\frac{1}{3} - \frac{1}{2} = \frac{2}{6} - \frac{3}{6}=-\frac{1}{6}; \\\frac{1}{4} - \frac{1}{3} = \frac{3}{12} - \frac{4}{12} = -\frac{1}{12}; \\\frac{1}{5} -\frac{1}{4} = \frac{4}{20} - \frac{5}{20} = -\frac{1}{20}$ There is no common difference so the given terms cannot be terms of an arithmetic sequence.
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