100 more than the sum of n consecutive integers is equal to the sum of the next n consecutive integers. Find n.

Guest Dec 6, 2019

#1**0 **

Since you're adding each number, n_{next}=99:

n_{x}=n_{x-1}+x | This is our basic formula

n_{x}=n_{x-1}+100 | We know that we're adding 100 to the current x, and the current x is equal to n_{x-1}+x, so the next x must be 100

n_{100}=n_{100-1}+100

n_{100}=n_{99}+100 | We subtract 1, giving us the previous x

Daewei Dec 6, 2019