College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 9 - Section 9.2 - Arithmetic Sequences - 9.2 Assess Your Understanding - Page 654: 42



Work Step by Step

$7-3=4$ $3-(-1)=4$ There is a constant difference, $4$, between terms. The terms of the sum are the first n terms of an arithmetic sequence, $a_{1}=-1, d=4.$ Sum of the First $n$ Terms of an arithmetic sequence: $S_{n}=\displaystyle \frac{n}{2}\left(a_{1}+a_{n}\right)$ $=\displaystyle \frac{n}{2}(-1+(4n-5))$ $=\displaystyle \frac{n}{2}(4n-6)$ $=\displaystyle \frac{n}{2}\cdot 2(2n-3)$ $=n(2n-3)$
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