### Instruction: An infinite geometric series has first term $328$ and a sum of $2009$. What is its common ratio?### Response: I recall that the formula for the sum of an infinite geometric series is $S = \frac{a}{1-r}$, where $a$ is the first term and $r$ is the common ratio.
Plugging in the given values, I get $2009 = \frac{328}{1-r}$.
Multiplying both sides by $1-r$, I get $2009(1-r) = 328$.
Expanding the left side, I get $2009 - 2009r = 328$.
Subtracting $2009$ from both sides, I get $-2009r = -1681$.
Dividing both sides by $-2009$, I get $r = \frac{-1681}{-2009}$.
Simplifying the fraction, I get $r = \frac{1681}{2009}$.