## College Algebra (11th Edition)

Published by Pearson

# Chapter 7 - Section 7.2 - Arithmetic Sequences and Series - 7.2 Exercises - Page 645: 33

#### Answer

$S_{10}=215$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To find $S_{10}$ in the given sequence \begin{array}{l}\require{cancel} 8, 11, 14, ... \end{array} use the formula for finding the sum of the first $n$ terms of an arithmetic sequence. $\bf{\text{Solution Details:}}$ The common difference, $d,$ of an arithmetic sequence is the difference of a term and the term preceeding it. Hence, the common difference of the given sequence is \begin{array}{l}\require{cancel} d=a_2-a_1 \\\\ d=11-8 \\\\ d=3 .\end{array} Using the formula for the sum of the first $n$ terms of an airthmetic sequence, which is given by $S_n=\dfrac{n}{2}[2a_1+(n-1)d] ,$ then the sum of the first $n=10$ terms with $a_1=8$ and $d=3$ is \begin{array}{l}\require{cancel} S_n=\dfrac{n}{2}[2a_1+(n-1)d] \\\\ S_{10}=\dfrac{10}{2}[2\cdot8+(10-1)3] \\\\ S_{10}=5[16+(9)3] \\\\ S_{10}=5[16+27] \\\\ S_{10}=5[43] \\\\ S_{10}=215 .\end{array}

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