solution: 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 $200 + 2d = \boxed{350}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  If the fourth term of an arithmetic sequence is $200$ and the eighth term is $500$, what is the sixth term?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 350
extra_info.question: If the fourth term of an arithmetic sequence is $200$ and the eighth term is $500$, what is the sixth term?
extra_info.split: test