Let the three consecutive numbers are x, x+1 and x+2. According to given conditions;

First number + Second number + Third number = 99

x + (x+1) + (x + 2) = 99

x + x + 1 + x + 2 = 99

3x + 3 = 99

3x = 99-3

3x= 96

x= 32

First number = x= 32

Second number= x + 1= 32 + 1 = 33

Third number = x + 2= 32 + 2= 34

First number + Second number + Third number = 99

x + (x+1) + (x + 2) = 99

x + x + 1 + x + 2 = 99

3x + 3 = 99

3x = 99-3

3x= 96

x= 32

First number = x= 32

Second number= x + 1= 32 + 1 = 33

Third number = x + 2= 32 + 2= 34