SOLUTION: hey tutor, i have a question on how to solve for 3 consecutive integers. i need help for my mid term review (homework) but have learned long ago so i forgot how to do it. 1. w

Question 699438: hey tutor,
i have a question on how to solve for 3 consecutive integers. i need help for my mid term review (homework) but have learned long ago so i forgot how to do it.
1. write an equation to find three consecutive integers with a sum of 66
2. write an equation to find three consecutive odd integers with a sum of 51
that's all. thank you! -olivia
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
When dealing with consecutive integers (or consecutive odd integers, or consecutive even integers),
you name one of them as your variable,
and write the other(s) number(s) as a function of the one you named.
Two consecutive integers could be named and .
Some strategies to name your integers seem to work better than others.

Three consecutive integers can be called , , and .
Their sum would be .
If that sum is --> -->
The three numbers are , , and .

Three consecutive odd integers (or three consecutive even integers) can be called
, and ,
because consecutive odd integers are 2 units apart (and so are consecutive even integers).
The sum of the three consecutive odd integers , and
is also .
If that sum is , then
--> -->
The three numbers are , , and .

NOTES: You could give your numbers different names.
I've tried other options before,
but I think my current choices work best.
Consecutive integers, consecutive odd integers, and consecutive even integers
are numbers in arithmetic sequence.
If you learned about arithmetic sequences,
you might remember that their median is their average.
The average of 3, or 5, or 7 (or any odd quantity of such numbers) is the number in the middle.
The sum is the average times the "quantity of such numbers".
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