Chapter 12 Sequences and Series - 12.2 Analyze Arithmetic Sequences and Series - 12.2 Exercises - Skill Practice - Page 807: 59

$15$

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 $S_n=-525$ Now, $-525=\dfrac{n \times (-7+(-3-4n))}{2}$ or, $2n^2+5n-525=0$ or, $(n-15) (2n+35)=0$ This gives: $n=\dfrac{-35}{2}; 15$ Hence, the positive solution for $n$ is $n=15$