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: 111

Answer

(i) The sequence is arithmetic. (ii) The next two terms are: $-49$ and $-63$.

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: $-7 - 7 = -14 \\-21 - (-7) = -21 + 7 = -14$ This means that the sequence has a common difference of $-14$. Thus, the sequence is $\underline{\text{arithmetic}}$. The next two terms can be found by adding $-14$ to the previous term. Therefore, the next two terms are: $-35 + (-14) = -49 \\-49 + (-14) = -63$
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