Averages of averages in Monte Carlo


I have a simulation set up as follows:

1,000 separate lives invest for 12, 24 and 36 months in three separate investment pots. The monthly returns are randomly generated from a defined normal distribution curve (using an expected arithmetic return average and standard deviation). The expected return/standard deviation assumptions are the same for each pot length. Each life, therefore, has three separate annualised (geometric) return values for their respective 12, 24 and 36-month pots.

I want to take an average across all lives for the returns of:

1. 12-month pots
2. 24-month pots
3. 36-month pots

Should I take an arithmetic or geometric average across the pots?

Many thanks :)