Answer
$-7920$
Work Step by Step
We have to determine the sum:
$S=\sum_{n=1}^{90} (3-2n)$
$S$ is the sum of an arithmetic sequence.
Determine its first term and the common difference:
$a_1=3-2(1)=1$
$d=(3-2(k+1))-(3-2k)=3-2k-2-3+2k=-2$
The number of terms is 90, so we have to determine the sum of the first $90$ terms. We use the formula:
$S_n=\dfrac{n(a_1+a_n)}{2}$
$a_1=1$
$a_{90}=3-2(90)=-177$
$\sum_{n=1}^{90} (3-2n)=\dfrac{90(1-177)}{2}=-7920$
