Precalculus: Mathematics for Calculus, 7th Edition

$-399$
See p. 855. For the arithmetic sequence $a_{n}=a+(n-1)d$ the nth partial sum $S_{n}=\displaystyle \sum_{k=1}^{n}[a+(k-1)d]$ is given by either of the following equivalent formulas: 1. $S_{n}=\displaystyle \frac{n}{2}[2a+(n-1)d]\qquad$2. $S_{n}=n(\displaystyle \frac{a+a_{n}}{2})$ ------------------- $\displaystyle \sum_{n=20}^{20}(1-2n)$. is a partial sum of an arithmetic series for which the first term is $a= 1-2\cdot 0=1$ and $d=-2$ There are $21$ terms in the sum (for n=0,1,2,...,20) The last term is $a_{21}=1-2\cdot 20=-39$. Using formula 2, $S_{21}=\displaystyle \frac{21}{2}(1-39)=-399$