SOLUTION: Hi, I know how to find the sum of n consecutive integers. I use the formula: n(n+1)/2 But my problem is: The sum of n consecutive integers is 120. Find n. My approach is n

Question 725436: Hi,
I know how to find the sum of n consecutive integers.
I use the formula: n(n+1)/2
But my problem is: The sum of n consecutive integers is 120. Find n.
My approach is nsq+n = 240
Now what is the easy way to find n?
I can do this by going from the answer to the question and guessing the number. But is there a easy way to find what n is.
Thanks,
Jay
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If you have studied polynomials and/or quadratic equations,
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At that point you would solve either
by factoring,
or by "completing the square",
or by using the quadratic formula.

However, it is easier to solve
by finding two consecutive numbers whose product is 240.

You could find factors from 1 up, and they would come in pairs:

7 is not a factor

9 is not a factor

and so on.

But if you have some factoring practice, the answer will jump at you.
It is obvious that = is the product of two consecutive numbers:
and
is what you would need to figure out to solve by factoring, anyway.
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