Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 11 - Section 11.2 - Arithmetic and Geometric Sequences - Exercise Set - Page 646: 27

Answer

$14, 10, $ and $6$ may be the first three terms of an arithmetic sequence because even though it may appear that we are subtracting $4$ instead of adding $4$ to get the next term, we are actually adding the common difference which is $-4$.

Work Step by Step

RECALL: An arithmetic sequence has a common difference $d$. The common difference can be found using the formula: $d=a_n- a_{n-1}$ where $a_{n-1}$ and $a_n$ are consecutive terms of the sequence $14, 10, $ and $6$ may be the first three terms of an arithmetic sequence because they have a common difference of $-4$. Note that: $10-14=-4$ and $6-10=-4$ Therefore, the numbers $14, 10,$ and $6$ may be the first three terms of an arithmetic sequence. It appears we are subtracting $4$ instead of adding $4$, but note that subtracting $4$ is the same as adding $-4$.
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