Chapter 12 Sequences and Series - 12.2 Analyze Arithmetic Sequences and Series - 12.2 Exercises - Skill Practice - Page 807: 58

$5$

For an arithmetic series, the sum for the finite series is given by: $S_n=\dfrac{n(a_1+a_n)}{2}$ We are given that $S_n=-50$ Now, $-50=\dfrac{n \times (0+5-5n)}{2}$ or, $n^2-n-20=0$ or, $(n-5) (n+4)=0$ This gives: $n=-4,5$ Hence, the positive solution for $n$ is $n=5$