# Chapter 7 - Section 7.2 - Arithmetic Sequences and Series - 7.2 Exercises - Page 646: 48

$S_{70}=4970$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To find the sum of the first $70$ positive even integers, use the formula for finding the sum of $n$ terms that form an arithmetic sequence. $\bf{\text{Solution Details:}}$ The sequence described by "the first $70$ positive even integers," is an arithmetic sequence with $a_1=2, d=2,$ and $n=70.$ 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 \begin{array}{l}\require{cancel} S_{70}=\dfrac{70}{2}[2(2)+(70-1)2] \\\\ S_{70}=35[4+(69)2] \\\\ S_{70}=35[4+138] \\\\ S_{70}=35[142] \\\\ S_{70}=4970 .\end{array}

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