Wednesday, May 8, 2013

19 consecutive numbers which sum is equal 95



If the question is: find 19 consecutive numbers whose sum is 95 then this is our solution:
Starting with n we write: n+(n+1)+(n+2)+...=95
As we can see this equation has 19 terms - quite long so let's use summation notation:

%0D%0A%0D%0Asum+%28n%2Bi+%2Ci=0%2C+18%29=95%0D%0A%0D%0A

The equation simplifies to:

%0D%0A19%2A%28n%2B9%29=95%0D%0A
which simplifies further to
%0D%0An%2B9=5%0D%0A%0D%0A
so n=-4 and our numbers are:
-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14

:)

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