Project Euler Problem #2 Solution

Problem

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.

Problem Description

A Fibonacci Sequence is a series in which each number is the sum of the two preceding ones.

The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144

In our problem, it is stated that the sequence starts with 1 and 2. And the first 10 terms would be, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89.

We want to find the Fibonacci sequence within 4 million and then find the sum of all the even numbers in that sequence.

Approach

This problem can be approached using a while loop and solved using the mathematical formula,

We need to find the Fibonacci Sequence that starts with 1 and 2, within 4 million. And our sequence looks like this, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ... < 4000000

Now, add the even numbers in the sequence, 2 + 8 + 34 + 144 + ... which will be our result.

Solution

let fn_1 = 1, // first
    fn_2 = 2, // second
    sum = 0;

while (fn_1 < 4000000) {
    if (fn_1 % 2 === 0) sum += fn_1; 

    let fn = fn_1 + fn_2; 
    [fn_1, fn_2] = [fn_2, fn];
}
console.time('p#2');
console.log(sum);
console.timeEnd('p#2');

Project Euler Problem #2 Solution

The GitHub repo for this problem is found at 02

If you have another or a better solution, please leave it in the comments below.

For the other Project Euler Solutions, please follow the series Project Euler Solutions in JS.

Thank you!

Project Euler: #2 - Even Fibonacci numbers

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