In the $n$th row of Pascal's Triangle where the first row is $n=0$, the arithmetic mean of the elements is $51.2$. What is the value of $n$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
In the $n$th row of Pascal's Triangle where the first row is $n=0$, the arithmetic mean of the elements is $51.2$. What is the value of $n$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
9
In the $n$th row of Pascal's Triangle where the first row is $n=0$, the arithmetic mean of the elements is $51.2$. What is the value of $n$?
train