Answer
$-7920$
Work Step by Step
We can see that there are $80$ terms and these terms are part of an arithmetic sequence, so we have:
$a_1=(3)-(2)(1)=1 \\ a_{90}=3-(2)(90)=-177$
There is a constant difference between the terms of:
$d=a_{n+1}-a_n=3-2(n+1) -(3-2n)=3-2n-2-3+2n=-2$
The sum of the first $n$ terms of an arithmetic sequence is given by:
$S_{n}= \dfrac{n}{2}\left(a_{1}+a_{n}\right) ..(1)$
Now, we plug in the above data into Equation-1 to obtain:
$S_{90}= \dfrac{90}{2}[1+(-177)] \\=(45)(-176) \\= -7920$
Therefore, the sum of the arithmetic sequence is: $-7920$.
