Even Values in the Fibonacci Sequence

Computer Science Level 2

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 to the maximum of four million, find the sum of the even terms in the sequence to this limit.

Hint: Use of a knowledge of programming might be helpful.

The answer is 4613732.

1 solution

Hunter Edwards
Oct 31, 2017

Here is my python Solution:

import time

def mat_sum(n):
    mat = [1,2]
    n1,n2 = 1,2
    while n1+n2 &lt; n:
        mat.append(n1+n2)
        n1,n2 = n2,n1+n2
    return sum(mat[1::3])

start = time.time()
for i in range(1000000): matsum = mat_sum(4000000)
elapsed = (time.time() - start)

print "result %s returned after %s seconds (1 million iterations)." % (matsum, elapsed)

The console output (with the time given for other reasons):

result 4613732 returned after 16.3734951019 seconds (1 million iterations).

Even Values in the Fibonacci Sequence

The answer is 4613732.

1 solution

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