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: 17

Answer

The sequence is geometric. The common ratio is $r=\dfrac{1}{2}$.

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: $\dfrac{\frac{3}{2}}{3} = \dfrac{3}{6}=\dfrac{1}{2} \\\dfrac{\frac{3}{4}}{\frac{3}{2}}=\dfrac{3}{4} \cdot \dfrac{2}{3} = \dfrac{1}{2} \\\dfrac{\frac{3}{8}}{\frac{3}{4}} = \dfrac{3}{8} \cdot \dfrac{3}{4}=\dfrac{1}{2}$ Since the ratio is common to all pairs of consecutive terms, then the sequence is geometric. The common ratio is $r=\dfrac{1}{2}$.
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