Chapter 11 - 11.2 - Arithmetic Sequences and Partial Sums - 11.2 Exercises - Page 786: 50

$S_n=S_{131}=-4585$

Integers from -100 to 30: $-100, -99, -98, ..., 28, 29, 30$ That is: $a_1=-100$, $a_n=30$ $d=-99-(-100)=-99+100=1$. Let's find $n$: $a_n=a_1+(n-1)d$ $30=-100+(n-1)1$ $30+100=n-1$ $130=n-1$ $n=131$ $S_n=\frac{n}{2}(a_1+a_n)$ $S_{131}=\frac{131}{2}(-100+30)=\frac{131}{2}(-70)=-4585$