The civclopedia says: "A unit gets its first promotion when achieving 2 XPs. The second promotion requires 3 additional XPs (for a total of 5), the third 4 more XPs (10 total), etc."

Excuse me, but I'm very confused. Isn't 5+4=9?!

According to Sullla's walkthrough promotion points are gained at 2/5/10/17 and so on. Though he also stated anything above 20 is rare. You'll notice it goes up by odd numbers. +3/+5/+7/...