Solving Project Euler Problem no.1 (Python)

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000.

mult3 = [] #multiples of 3
mult5 = [] #multiples of 5
for i in range(1000):  
    if i % 3 == 0 and i % 5 != 0: #make sure its numbers are divisible by 3 but not 5
        mult3.append(i)
    if i % 5 == 0 and i % 3 != 0: #make sure its numbers are divisible by 5 but not 3
        mult5.append(i)

total3 = sum(mult3) #sum of all elements in mult3
total5 = sum(mult5) #sum of all elements in mult5
print(total3 + total5)

I was wrong with the answer of 200003. Had I misunderstood the question or are there any bugs in my code?
Link to the original question

Answer

You can take the iterative approach: O(n)

s35 = sum(n for n in range(1000) if n%3 == 0 or n%5 == 0)

Or you can compute it mathematically: O(1)

n3  = (1000-1)//3    # number of multiples of 3  (includes multiples of 15)
n5  = (1000-1)//5    # number of multiples of 5  (includes multiples of 15)
n15 = (1000-1)//15   # number of multiples of 15 (counted twice)

s35 =  n3*(n3+1)//2*3 + n5*(n5+1)//2*5 - n15*(n15+1)//2*15