Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:
$1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...$
By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.
In [1]:
f0 = 0
f1 = 1
total = 0
while f1 < 4000000:
f0, f1 = f1, f0 + f1
if f1 % 2 == 0:
total += f1
print(total)
Note that every third Fibonacci number is even. We could also use the formula $$F(3) + F(6) + F(9) + \cdots + F(3n) = (F(3n+2)-1)/2$$ https://oeis.org/A099919