Chapter 8, Sequences and Series - Section 8.2 - Arithmetic Sequences - 8.2 Exercises - Page 607: 64

$S_{21}=-399$

We are given: $\sum_{n=0}^{20}(1-2n)$ Since the values go down by $-2$ consistently, this is an arithmetic sequence. We find the first and last values of the sequence: $a_0=1-2*0=1$ $a_{20}=1-2*20=-39$ Thus the partial sum is: $S_{21}=\frac{21}{2}(1+-39)=-399$