Chapter 8, Sequences and Series - Section 8.2 - Arithmetic Sequences - 8.2 Exercises - Page 608: 75

$n=20$

We know the sequence is: $15, 18, 21$ ... This is an arithmetic sequence with $a_1=15$ and $d=3$. We need to find $n$ so that $S_n=870$. $S_n=\frac{n}{2}[2a_1+(n-1)d]$ $870=\frac{n}{2}[2*15+(n-1)3]$ $870=\frac{n}{2}[30+3n-3]$ $870=\frac{n}{2}[27+3n]$ $1740=n(27+3n)$ $1740=27n+3n^2$ $3n^2+27n-1740=0$ $n^2+9n-580=0$ $(n-20)(n+29)=0$ $(n-20)=0$ or $(n+29)=0$ $n=20$ or $n=-29$ The number of rows can't be negative, so $n=20$.