The sum of the first n positive integers is equal to 1/2(n squared+n). How many of the first n positive integers must be added to give a sum of 325?

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Vin Ginge Profile
Vin Ginge answered
The required equation is, 325 = 1/2(n2 + n)...then 650 = n2 + n...and the equation can be written:-
n2 + n - 650 = 0...which can be factored
(n + 26)(n - 25) = 0
As we are only concerned with a positive integer solution, this occurs when n - 25 = 0, thus n = 25
Check : 1/2(252 + 25) = 1/2(625 + 25) = 325

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