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First find the number which is 1/3 of 51. This is 17. Thus any three numbers which average 17 will always add up to 51. For the numbers to be consecutive and have an average of 17, the middle number must be 17 and the two remaining numbers are 17-1 and 17+1 ie 16 and 18. So the three consecutive numbers are 16, 17 and 18.
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