#### Answer

$n=20$

#### Work Step by Step

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 $n=20$.