49+50+51=150
General rule for this kind of question: divide the number you're trying to obtain (150) by the number of integers you're allowed (3), and then simply add one and subtract one until you have the specified number of integers.
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The numbers are 148, 150 and 152.
There is no set of three consecutive integers whose sum is 71.
The sum of three consecutive integers is -72
The three integers are 187, 188 and 189.
The sum of any three consecutive odd integers is going to give an odd result. It is impossible for the sum of an odd number of odd integers to equal an even number.