Answer
$S_{50}=2,500$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the sum of the first $
50
$ positive odd 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 $50$ positive odd integers," is an arithmetic sequence with $a_1=1, d=2,$ and $n=50.$
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_{50}=\dfrac{50}{2}[2(1)+(50-1)2]
\\\\
S_{50}=25[2+(49)2]
\\\\
S_{50}25[2+98]
\\\\
S_{50}=25[100]
\\\\
S_{50}=2,500
.\end{array}
