Answer
$6080$
Work Step by Step
We have to determine the sum:
$S=\sum_{n=1}^{80} (2n-5)$
$S$ is the sum of an arithmetic sequence.
Determine its first term and the common difference:
$a_1=2(1)-5=-3$
$d=(2(k+1)-5)-(2k-5)=2k+2-5-2k+5=2$
The number of terms is 80.
Therefore the given sum contains $80$ terms, so we have to determine the sum of the first $80$ terms. We use the formula:
$S_n=\dfrac{n(a_1+a_n)}{2}$
$a_1=-3$
$a_{80}=2(80)-5=155$
$\sum_{n=1}^{80} (2n-5)=\dfrac{80(-3+155)}{2}=6080$
