Answer
$S_{90}=8,100$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the sum of the first $
90
$ 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 $90$ positive odd integers," is an arithmetic sequence with $a_1=1, d=2,$ and $n=90.$
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_{90}=\dfrac{90}{2}[2(1)+(90-1)2]
\\\\
S_{90}=45[2+(89)2]
\\\\
S_{90}=45[2+178]
\\\\
S_{90}=45[180]
\\\\
S_{90}=8,100
.\end{array}
