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

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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(5399) About Me  (Show Source):
You can put this solution on YOUR website!
If you have studied polynomials and/or quadratic equations,
n%5E2%2Bn=240 <--> n%5E2%2Bn-240=0
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 n%28n%2B1%29=240
by finding two consecutive numbers whose product is 240.

You could find factors from 1 up, and they would come in pairs:
240=1%2A240
240=2%2A120
240=3%2A80
240=4%2A60
240=5%2A48
240=6%2A40
7 is not a factor
240=8%2A30
9 is not a factor
240=10%2A24
and so on.

But if you have some factoring practice, the answer will jump at you.
It is obvious that 240=8%2A30%7D%7D%2C+right%3F%0D%0A%7B%7B%7B240=8%2A30=%288%2A2%29%2A%2830%2F2%29=16%2A15 is the product of two consecutive numbers:
highlight%28n=15%29 and highlight%28n%2B1=16%29
240=16%2A15 is what you would need to figure out to solve n%5E2%2Bn-240=0 by factoring, anyway.