Consecutive numbers are numbers that follow one right after the other. One example is the set {6, 7, 8}. We don't know the three consecutive numbers so let's define...
x = first number x+1 = second number x+2 = third number
where x, x+1, and x+2 are consecutive numbers
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"The sum of three consecutive numbers is -15" meaning that x+(x+1)+(x+2) = -15
Let's solve for x x+(x+1)+(x+2) = -15 x+x+1+x+2 = -15 3x+3 = -15 3x+3-3 = -15-3 3x = -18 3x/3 = -18/3 x = -6
So this means
first number = x = -6 second number = x+1 = -6+1 = -5 third number = x+2 = 6+2 = -4
The list of consecutive values is {-6, -5, -4}
They add up to (-6) + (-5) + (-4) = -11+(-4) = -15 which confirms we have the right values
