Answer
$n=25$
Work Step by Step
We are told that we have an arithmetic sequence with:
$a=12$ and $d=8$
We know that the sum of such a sequence is:
$S_n=\frac{n}{2}[2*a+(n-1)d]$
We with the sum to equal $2700$:
$2700=\frac{n}{2}[2*12+(n-1)*8]$
$5400=n(24+8n-8)$
$5400=n(16+8n)$
$5400=16n+8n^2$
$8n^2+16n-5400=0$
$4n^{2}+8n-2700=0$
$4(n+27)(n-25)=0$
$(n+27)=0$ or $(n-25)=0$
$n=-27$ or $n=25$
But $n$ can not be negative, so the answer is $n=25$.
