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: 114

Answer

(i) The sequence is geometric. (ii) The next two terms are: $9\sqrt3$ and $27$.

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: $3 \div \sqrt3 = \sqrt3 \\3\sqrt3 \div 3 = \sqrt3$ This means that the sequence has a common ratio of $\sqrt3$. Thus, the sequence is $\underline{\text{geometric}}$. The next two terms can be found by multiplying $\sqrt3$ to the previous term. Therefore, the next two terms are: $9 \times \sqrt3 = 9\sqrt3 \\9\sqrt3 \times \sqrt3 = 9(3) = 27$
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