If the average of 3 numbers is 37 then the sum of those numbers = 37 * 3 = 111. Which is an odd number. Adding together even numbers never results in an odd number. Therefore the 3 numbers can not be even numbers; consecutive or otherwise. The question can not be answered.
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The numbers are 37, 38, 39 and 40.
11,12,13
117
I can find 5: 37 (in a sequence of 2) ie 37 + 38 24 (3) 13 (5) 10 (6) 3(10)
37 and 38