Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 11 - Sequences; Induction; the Binomial Theorem - Chapter Test - Page 860: 11

Answer

The sequence is neither geometric nor arithmetic.

Work Step by Step

For the sequence to be geometric, the quotient of all consecutive terms must be constant. Here, we have: $\dfrac{a_{2}}{a_1}=\dfrac{1/5}{-1/3}$ and $\dfrac{a_{3}}{a_2}=\dfrac{3/7}{1/5}$ This shows that the quotient of all consecutive terms is not constant and thus it is not a geometric sequence. In order for the sequence to be arithmetic, the difference of all consecutive terms must be constant. Here, we have: $a_2-a_1= \dfrac{3}{7}-\dfrac{1}{5} \ne a_3-a_2=\dfrac{1}{5}-\dfrac{-1}{3}$ This shows that the difference of all consecutive terms is not constant and thus it is not an arithmetic sequence. Hence, the sequence is neither geometric nor arithmetic.
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