SOLUTION: The sum of three consective odd integers is -3, what is the largest odd integer? The sum of three consective integers is 0. What is the smallest integer?

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Question 650861: The sum of three consective odd integers is -3, what is the largest odd integer?
The sum of three consective integers is 0. What is the smallest integer?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
1.
If we start with an odd number and each number in the sequence is 2 more than the previous number then we will get consecutive odd integers.
if first one is x, second one will be x%2B2, and third one will be x%2B4
the sum is: x%2B%28x%2B2%29%2B%28x%2B4%29=-3
x%2B%28x%2B2%29%2B%28x%2B4%29=-3...solve for x
3x%2B6=-3
3x=-3-6
3x=-9
x=-9%2F3
highlight%28x=-3%29....first number
second one will be x%2B2...->...-3%2B2 ...->...highlight%28-1%29
third one will be x%2B4...->...-3%2B4 ...->...highlight%281%29

so, the numbers are:highlight%28-3%29,highlight%28-1%29, and highlight%281%29; as you can see, the greatest one is highlight%281%29

2.
The sum of three consecutive integers is 0. What is the smallest integer?
If we start with an integer, each next consecutiveinteger in the sequence is 1 more than the previous one
if first one is x, second one will be x%2B1, and third one will be x%2B2
the sum is: x%2B%28x%2B1%29%2B%28x%2B2%29=0...solve for x
3x%2B3=0
3x=-3
x=-3%2F3
highlight%28x=-1%29
second one will be x%2B1...->...-1%2B1 ...->...highlight%280%29
third one will be x%2B2...->...-1%2B2 ...->...highlight%281%29

so, the numbers are:highlight%28-1%29,highlight%280%29, and highlight%281%29; as you can see, the smallest integer is highlight%28-1%29