Sum of even Fibbonacci

Computer Science Level 3

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 1, the first 10 terms will be:

1,1, 2, 3, 5, 8, 13, 21, 34, 55 .....

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

Try other problems here .

The answer is 4613732.

1 solution

Rishabh Deep Singh
May 27, 2017

public class Main {
    public static void main(String[] args) {
        int old=1,present=2,next;
        int sum=0;
        while(present<4_000_000){
            if (present%2==0) {
                sum += present;
            }
            next = old + present;
            old = present;
            present=next;
        }
        System.out.println("the Sum is: " + sum);
    }

}

Do you know how to use the theory of fibonacci sequence to answer this problem directly?

Hint: Every third number is even.

Calvin Lin Staff - 4 years ago

Sum of even numbers is half of sum of all numbers. )))

Hasmik Garyaka - 3 years, 8 months ago

Great insights. That allows us to conclude that the sum of the even terms up to $F_{3n}$ is $\frac{ F_{3n+2} - 1 } { 2}$ .

Alternatively, we can use Binet's formula and sum up the Geometric progressions accordingly.

Calvin Lin Staff - 3 years, 8 months ago

And sum(from 1 to n)=F(n + 2) - 1.

Hasmik Garyaka - 3 years, 8 months ago

Sum of even Fibbonacci

The answer is 4613732.

1 solution

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