Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 814: 51



Work Step by Step

We have to determine the sum: $S=\sum_{n=1}^{80} (2n-5)$ $S$ is the sum of an arithmetic sequence. Determine its first term and the common difference: $a_1=2(1)-5=-3$ $d=(2(k+1)-5)-(2k-5)=2k+2-5-2k+5=2$ The number of terms is 80. Therefore the given sum contains $80$ terms, so we have to determine the sum of the first $80$ terms. We use the formula: $S_n=\dfrac{n(a_1+a_n)}{2}$ $a_1=-3$ $a_{80}=2(80)-5=155$ $\sum_{n=1}^{80} (2n-5)=\dfrac{80(-3+155)}{2}=6080$
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