Chapter 12 Sequences and Series - 12.2 Analyze Arithmetic Sequences and Series - 12.2 Exercises - Skill Practice - Page 807: 56

$n=8$

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 $S_n=-28$ Now, $-28=\dfrac{n \times (7+10-3n)}{2}$ or, $3n^2-17n-56=0$ or, $(n-8) (3n+7)=0$ This gives: $n=8, \dfrac{-7}{3}$ Hence, the positive solution for $n$ is $n=8$.