I believe OFFSET makes it simpler, for example, assuming you want the first average in cell D2. Copy down this formula in D2.
=AVERAGE(OFFSET(B$3:B$5,3*(ROWS(D$2:D2)-1),0))
Generally speaking, the B$3:B$5 range indicates the first range you want to average, 3 is the number of rows to increment each time, and D2 is the start cell. Any or all of those can be altered, though, based on your specific requirements.