Applications: Number problems and consecutive integers

Sum of 3 consecutive odd integers is -3, what are the integers?


Solution


A number is odd if it has the following format: 2n + 1



Let 2n + 1 be the first odd integer

Let 2n + 3 be the second odd integer

Let 2n + 5 be the third odd integer



Since the sum is equal to -3, we get the following equation:


2n + 1 + 2n + 3 + 2n + 5 = -3


2n + 2n + 2n + 1 + 3 + 5 = -3


6n + 9 = -3


6n + 9 - 9 = -3 - 9


6n + 0 = -12


6n = -12


Divide both sides by 6


6n / 6 = -12 / 6



n = -2


The first odd integer is 2n + 1 = 2 × -2 + 1 = -4 + 1 = -3



The second odd integer is 2n + 3 = 2 × -2 + 3 = -4 + 3 = -1



The third odd integer is 2n + 5 = 2 × -2 + 5 = -4 + 5 = 1


The 3 consecutive odd integers are -3, -1, and 1


Indeed -3 + -1 + 1 = -3 + 0 = -3


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