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: 113


(i) The sequence is geometric. (ii) The next two terms are: $25\sqrt5$ and $125$.

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: $5 \div \sqrt5 = \sqrt5 \\5\sqrt5 \div 5 = \sqrt5$ This means that the sequence has a common ratio of $\sqrt5$. Thus, the sequence is $\underline{\text{geometric}}$. The next two terms can be found by multiplying $\sqrt5$ to the previous term. Therefore, the next two terms are: $25 \times \sqrt5 = 25\sqrt5 \\25\sqrt5 \times \sqrt5 = 25(5) = 125$
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