Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.7 Arithmetic and Geometric Sequences - Exercise Set 5.7 - Page 330: 108


(i) The sequence is arithmetic. (ii) The next two terms are: $2$ and $\frac{7}{3}$.

Work Step by Step

A sequence is: (a) arithmetic if there is a common difference among the terms. (b) geometric if there is a common ratio among the terms. Notice that the given sequence has terms that increase by $\frac{1}{3}$. This means that the sequence has a common difference of $\frac{1}{3}$. Thus, the sequence is $\underline{\text{arithmetic}}$. The next two terms can be found by adding $\frac{1}{3}$ to the previous term. Therefore, the next two terms are: $\frac{5}{3} + \frac{1}{3} =\frac{6}{3}=2 \\2 + \frac{1}{3} = \frac{7}{3}$
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