If this is meant to be an arithmetic progression then the common difference is 2a-b-a-b=a-2b. The next term would therefore be 2a-b+a-2b=3a-3b, then 3a-3b+a-2b=4a-5b, then 4a-5b+a-2b=5a-7b. The series would be:
a+b, 2a-b, 3a-3b, 4a-5b, 5a-7b.
I'm not sure if this is what you're looking for.
The arithmetic mean of each pair of terms would be:
3a/2, 5a/2-2b, 7a/2-4b, 9a/2-6b.