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 - Page 614: 14

Answer

The ratios are different so the given sequence is not geometric.

Work Step by Step

A geometric sequence has a common ratio $r$. The common ratio is multiplied to the current term to get the next term of the sequence. The common ratio is equal to the the quotient of a term and the term before it. Solve for the ratio of each pair of consecutive terms to obtain: $\dfrac{48}{3} = 16 \\\dfrac{93}{48}=\dfrac{31}{16} \\\dfrac{138}{93} = \dfrac{46}{31}$ Since the ratio is common to all pairs f consecutive terms, then the sequence is geometric. The ratios are different so the given sequence is not geometric.
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