100 more than the sum of n consecutive integers is equal to the sum of the next n consecutive integers. Find n.
Since you're adding each number, nnext=99:
nx=nx-1+x | This is our basic formula
nx=nx-1+100 | We know that we're adding 100 to the current x, and the current x is equal to nx-1+x, so the next x must be 100
n100=n99+100 | We subtract 1, giving us the previous x