Answer
$S_{80}=3,240$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the sum of the first $
80
$ positive numbers, use the formula for finding the sum of $n$ terms that form an arithmetic sequence.
$\bf{\text{Solution Details:}}$
The arithmetic sequence described by "the first $80$ positive integers," has $a_1=1, a_{80}=80,$ and $n=80.$
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
\begin{array}{l}\require{cancel}
S_{80}=\dfrac{80}{2}(1+80)
\\\\
S_{80}=40(81)
\\\\
S_{80}=3,240
.\end{array}