If the fourth term of an arithmetic sequence is $200$ and the eighth term is $500$, what is the sixth term?
The sixth term is exactly halfway between the fourth and the eighth in the arithmetic sequence, so it is the average of the two terms. Therefore, the sixth term is $(200 + 500)/2 = \boxed{350}$.  We also could have found the common difference by noting that there are four steps between the fourth term and the eighth term.  So, if $d$ is the common difference, we have $4d = 500-200 = 300$. Therefore, we find $d=75$.  The sixth term is two steps after the fourth, or $200 + 2d = \boxed{350}$.