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: 18

Answer

The sequence is geometric. The common ratio is $r=-\dfrac{1}{3}$.

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{-9}{27} = -\dfrac{1}{3} \\\dfrac{3}{-9}=-\dfrac{1}{3} \\\dfrac{-1}{3} = -\dfrac{1}{3} $ Since the ratio is common to all pairs of consecutive terms, then the sequence is geometric. The common ratio is $r=-\dfrac{1}{3}$.
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