SOLUTION: If 400 more than the sum of p consecutive integers is equal to the sum of the next p consecutive integers, what is the value of p?

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Question 1191491: If 400 more than the sum of p consecutive integers is equal to the sum of the next p consecutive integers, what is the value of p?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.
If 400 more than the sum of p consecutive integers is equal
to the sum of the next p consecutive integers, what is the value of p?
~~~~~~~~~~~~~~~~ 

Let x be the arithmetic mean of that (first mentioned) p consecutive integers.

Then the sum of that (first mentioned) p consecutive integers is x*p.


The average of the next p consecutive integers is  (x+p),

and the sum of the next p consecutive integers is (x+p)*p.


So, we have this equation

    (x+p)*p = x*p + 400

     xp + p^2 = xp + 400

          p^2 = 400

          p   = 20.


ANSWER.  p = 20.

Solved.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


If you have p consecutive integers and then you have the following p consecutive integers, then each integer in the second set is p more than the corresponding integer in the first set.

So the difference between the sum of the p integers in the second set and the sum of the p integers in the first set is p times p, which is p squared.

Give that that difference is 400, we have p^2=400 so p=20.

ANSWER: 20
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