2009 Seat Ibiza battery is always dying after only 1 week

This needs what is known as a parasitic draw test.
There's a number of these on Youtube,
Basically it's testing for current/voltage when the cars off.

Get your alternator output checked , if faulty it will cause battery drain as power taken from battery when running wont be getting replaced .

Thanks for your answers! Do you know approximately how much will it cost to check the alternator and to do the parasitic draw test?
How much would it cost to change the alternator, just asking because being a woman sometimes I feel the garage give a higher price!

Hmm a bit of a difficult one to answer that.
Well the alternator times out at around an hour if that's the fault.
The draw test depends,
If and I stress if the current draw is there when being tested the all well and good,
But some cars have active modules like the alarm system that doesn't come alive for a certain time.
Best to say an auto spark will start by charging an hours labour to test the charging system and draw test it.
But like I stated if the current draw isn't apparent the time will roll on until it's found.
Electrics can be a pig,
10n hours to find a fault that take ten mins to fix kind of thing!!
But an hours labour is where it will start.
And fingers crossed it will be enough.

Any fast fit centre or the likes of Halfords should normally carry out this simple test on alternator output while you wait if you ask nicely .Surprised if they would charge you , I never did with any of my customers .