Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 14 - Sequences, Series, and the Binomial Theorem - 14.2 Arithmetic Sequences and Series - 14.2 Exercise Set - Page 902: 34



Work Step by Step

The first n term of an arithmetic sequence can be calculated as: $S_n=\frac{n}{2}(a_1+a_n)$ We have to find $a_{14}$ in order to find the sum. First, $d$ can be calculated as the difference of subsequent terms: $d=a_2-a_1=7-11=-4$ $a_{14}=a_1+ d(14-1)=11+(-4)\times13=11-52=-41$ By substituting in the formula of the sum, we get: $S_{14}=\frac{14}{2}(11+(-41))=7\times(-30)=-210$
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