9. Define $a_{n}=1+3+3^{2}+\cdots+3^{n}$ ( $n$ is a positive integer), for example: $a_{4}=1+3+3^{2}+3^{3}+3^{4}$. How many numbers among $a_{1}, a_{2}, \cdots, a_{2013}$ are multiples of 7?
【Analysis】 $a_{n}=1+3+3^{2}+\cdots+3^{n}=\frac{3^{n+1}-1}{2}$, that is, as long as $3^{n+1}-1$ is a multiple of 7, $a_{n}$ is a multiple of 7. It is found that the remainder of $3^{n+1}$ divided by 7 cycles through $2, 6, 4, 5, 1, 3$. $2013 \cdots 6=335 \cdots 3$
Therefore, there are 335 numbers that leave a remainder of 1 when divided by 7, meaning that among $a_{1}, a_{2}, \cdots, a_{2013}$, there are 335 multiples of 7.