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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