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: 112

Answer

(i) The sequence is arithmetic. (ii) The next two terms are: $-42$ and $-54$.

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: $-6-6 = -12 \\-18 - (-6) = -18 +6 = -12$ This means that the sequence has a common difference of $-12$. Thus, the sequence is $\underline{\text{arithmetic}}$. The next two terms can be found by adding $-12$ to the previous term. Therefore, the next two terms are: $-30 + (-12) = -42 \\-42 + (-12) = -54$
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