SOLUTION: What is the sum of three consecutive odd integers if the sum of the second and third numbers is six more than two times the first number?

Question 158713: What is the sum of three consecutive odd integers if the sum of the second and third numbers is six more than two times the first number?

Answer by SAT Math Tutor(36) (Show Source): You can put this solution on YOUR website!
Any odd number can be written as 2n+1 for some integer, n. So, the sum of 3 consecutive odd integers is 2n+1 + 2n+3 + 2n+5.
Then, we are told that 2(2n+1) + 6 = 2n+3 + 2n+5
So, 4n + 2 + 6 = 4n + 8
Or, 4n + 8 = 4n + 8
Any value of n obviously satisfies this equation so we have a triviality (ie. n can equal anything).
Therefore, there is not one answer.
2n+1 + 2n+3 + 2n+5 = 6n + 9 so we could say in set notation the answer lies in the set {6n + 9 | n is an integer}

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