Python solution for Project Euler's problem #1

Problem 1 - Multiples of 3 and 5

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.

Iterative solution

it gets very slow for 1,000,000 because its time complexity is O(n) (linear)

def sum(maximum, multiplier):
    sum = 0
    for x in range(multiplier, maximum, multiplier):
        sum += x
    return sum
    
target = 1000
print sum(target, 3) + sum(target, 5) - sum(target, 3 * 5)

Fastest solution

it never gets slow because its time complexity is O(1) (constant)

def sum(maximum, interval):
    maximum -= 1
    an = maximum - (maximum % interval)
    n = int(maximum / interval)
    return n * (interval + an) / 2
        
target = 1000
print sum(target, 3) + sum(target, 5) - sum(target, 3 * 5)