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: 39

Answer

$n^{2}$

Work Step by Step

$5-3=3-1=2$ there is a constant difference between terms. The terms of the sum make up an arithmetic sequence, $a_{1}=1, d=2.$ Sum of the First $n$ Terms of an arithmetic sequence: $S_{n}=\displaystyle \frac{n}{2}\left(a_{1}+a_{n}\right)$ $=\displaystyle \frac{n}{2}(1+(2n-1))$ $=\displaystyle \frac{n}{2}(2n)$ $=n^{2}$
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