Let's called the first integer x. The second would be x+1 and the third x+2. Adding all these integers together would result in 114:
x+(x+1)+(x+2)=114
x+x+1+x+2=114
3x+3=114
Subtract 3 from both sides:
3x=111
Divide both sides by 3:
x=37
The first number is 37, so the three numbers are 37, 38, and 39.
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117
-1, -3, -5
Start with "-3", then add one at a time to get as many consecutive integers as you want.
There are no consecutive odd integers whose sum is equal to 35. 9+11+13 = 33, and 11+13+15 = 39.
It need not be. 2 and 3 are consecutive integers and their sum is 5, not 31.