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: 43



Work Step by Step

$2+4+6+\cdots+70=2+(2+2)+(2+2\cdot 2)+\cdots+(2+34\cdot 2)$ $4-2=2$ $6-4=2$ There is a constant difference, $2$, between terms. The terms of the sum are the first $35$ terms of an arithmetic sequence, $a_{1}=2, d=4.$ Sum of the First $n$ Terms of an arithmetic sequence: $S_{n}=\displaystyle \frac{n}{2}\left(a_{1}+a_{n}\right)$ $S_{35}=\displaystyle \frac{35}{2}\left(2+70\right)$ $S_{35}=35\cdot 36=1260$
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