I hope I've put this in the right place but I have a coolant loss problem that I'm struggling to solve. I recently bought an Audi A3 2012 model 1.6tdi just over a year old with 37k on the clock. Thinks it's been a reps car. Bought it from a reputable dealer (JCT 600, UK company) , but after less than a month got a coolant warning. Sure enough was almost empty. I topped it up and made sure the cap was on tight, but a week later it's almost back to low. I'm worried as I'm no mechanic. I'm taking it into Audi as it's in warranty till 2015.
What could it be? And do I need to ask Audi to look at specific things?

Some extra info: I have found no visible patched under the car, but it's been wet so that's hampering me.
The car has been serviced by Audi at around 18k and by JCT (who use Audi parts to maintain warranty) at 36k.

 

Update: I needed a new water pump. Does the fact that a water pump needs replacing point to other problems, or should I be ok now?