Answer
$S_{120}=7,260$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the sum of the first $
120
$ 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 $120$ positive integers," has $a_1=1, a_{120}=120,$ and $n=120.$
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_{120}=\dfrac{120}{2}(1+120)
\\\\
S_{120}=60(121)
\\\\
S_{120}=7,260
.\end{array}
