The median of a set of consecutive positive integers is equal to the mean of the set of integers.  Therefore, we can find the median by dividing the sum by the number of integers: $3^7/3^3=3^4=\boxed{81}$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The sum of 27 consecutive positive integers is $3^7$. What is their median?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
81
The sum of 27 consecutive positive integers is $3^7$. What is their median?
test