College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 7 - Section 7.2 - Arithmetic Sequences and Series - 7.2 Exercises - Page 646: 44



Work Step by Step

$\bf{\text{Solution Outline:}}$ To find the sum of the first $ 120 $ positive numbers, use the formula for finding the sum of $n$ terms that form an arithmetic sequence. $\bf{\text{Solution Details:}}$ The arithmetic sequence described by "the first $120$ positive integers," has $a_1=1, a_{120}=120,$ and $n=120.$ Using the formula for the sum of the first $n$ terms of an airthmetic sequence, which is given by $ S_n=\dfrac{n}{2}(a_1+a_n) ,$ then \begin{array}{l}\require{cancel} S_{120}=\dfrac{120}{2}(1+120) \\\\ S_{120}=60(121) \\\\ S_{120}=7,260 .\end{array}
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