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 645: 40



Work Step by Step

$\bf{\text{Solution Outline:}}$ To find $S_{10}$ in the given sequence \begin{array}{l}\require{cancel} a_1=-8, a_{10}=-1.25 \end{array} use the formula for finding the sum of the first $n$ terms of an arithmetic sequence. $\bf{\text{Solution Details:}}$ 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 the sum of the first $n=10$ terms with $a_1=-8$ and $a_{n}=-1.25$ is \begin{array}{l}\require{cancel} S_n=\dfrac{n}{2}[a_1+a_n] \\\\ S_{10}=\dfrac{10}{2}[-8+(-1.25)] \\\\ S_{10}=\dfrac{10}{2}[-8-1.25] \\\\ S_{10}=5[-9.25] \\\\ S_{10}=-46.25 .\end{array}
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