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: 52



Work Step by Step

We have to determine the sum: $S=\sum_{n=1}^{90} (3-2n)$ $S$ is the sum of an arithmetic sequence. Determine its first term and the common difference: $a_1=3-2(1)=1$ $d=(3-2(k+1))-(3-2k)=3-2k-2-3+2k=-2$ The number of terms is 90, so we have to determine the sum of the first $90$ terms. We use the formula: $S_n=\dfrac{n(a_1+a_n)}{2}$ $a_1=1$ $a_{90}=3-2(90)=-177$ $\sum_{n=1}^{90} (3-2n)=\dfrac{90(1-177)}{2}=-7920$
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