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: 105


(i) The sequence is geometric. (ii) The next two terms are: $\frac{3}{16}$ and $\frac{3}{32}$.

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 in the given sequence: $\frac{3}{2} \div 3 = \frac{1}{2} \\\\\frac{3}{4} \div \frac{3}{2} = \frac{1}{2}$ This means that the sequence has a common ratio of $\frac{1}{2}$. Thus, the sequence is $\underline{\text{geometric}}$. The next two terms can be found by multiplying $\frac{1}{2}$ to the previous term. Therefore, the next two terms are: $\frac{3}{8} \times \frac{1}{2} = \frac{3}{16} \\\frac{3}{16} \times \frac{1}{2}=\frac{3}{32}$
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