Answer
$S_{70}=4970$
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}
