An infinite geometric series has first term $328$ and a sum of $2009$. What is its common ratio?

S = F / [1 - R] 

2009 = 328 / [1 - R]

 

Solve for R:
328/(1 - R) = 2009

Take the reciprocal of both sides:
(1 - R)/328 = 1/2009

Multiply both sides by 328:
1 - R = 8/49

Subtract 1 from both sides:
-R = -41/49

Multiply both sides by -1:
R = 41/49

2009 = 328/(1 - r)

 

Solve for r, and there you go! :)

This is using the formula:

S = term1/(1 - r)