The sum of three consecutive integer is is - 34

The integer are called, a, b, c

if they are consecutive that means that:

b = a + 1

c = a + 2

and we know that they add to - 34, that is:

a + b + c = - 34

lets substitute the first two equations in the third:

a + b + c = - 34

a + (a + 1) + (a + 2) = - 34

3a + 3 = - 34

3a = - 37

a = - 37/3

the first number is - 37/3, therefore there aren't integers consecutive that sum - 34