# Even Fibonacci Numbers Sum

Given a limit, find the sum of all the even-valued terms in the Fibonacci sequence below given limit.

The first few terms of Fibonacci Numbers are, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ,… (Even numbers are highlighted).

Examples :

Input : limit = 8
Output : 10
Explanation : 2 + 8 = 10

Input : limit = 400;
Output : 188.
Explanation : 2 + 8 + 34 + 144 = 188.

## Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

A simple solution is to iterate through all prime numbers while the next number is less than or equal to given limit. For every number, check if it is even. If the number is even, add it to the result.

An efficient solution is based on the below recursive formula for even Fibonacci Numbers

Recurrence for Even Fibonacci sequence is:
EFn = 4EFn-1 + EFn-2
with seed values
EF0 = 0 and EF1 = 2.

EFn represents n'th term in Even Fibonacci sequence.

Refer this more details of above formula.

So while iterating over Fibonacci numbers, we only generate even Fibonacci numbers.

## C++

 // Find the sum of all the even-valued terms in // the Fibonacci sequence which do not exceed // given limit. #include using namespace std;    // Returns sum of even Fibonacci numbers which are // less than or equal to given limit. int evenFibSum(int limit) {     if (limit < 2)         return 0;        // Initialize first two even prime numbers     // and their sum     long long int ef1 = 0, ef2 = 2;     long long int sum = ef1 + ef2;        // calculating sum of even Fibonacci value     while (ef2 <= limit)     {         // get next even value of Fibonacci sequence         long long int ef3 = 4*ef2 + ef1;            // If we go beyond limit, we break loop         if (ef3 > limit)             break;            // Move to next even number and update sum         ef1 = ef2;         ef2 = ef3;         sum += ef2;     }        return sum; }    // Driver code int main() {     int limit = 400;     cout << evenFibSum(limit);     return 0; }

## Java

 // Find the sum of all the even-valued terms in // the Fibonacci sequence which do not exceed // given limit. import java.io.*;    class GFG  {     // Returns sum of even Fibonacci numbers which are     // less than or equal to given limit.     static int evenFibSum(int limit)     {         if (limit < 2)             return 0;                // Initialize first two even prime numbers         // and their sum         long ef1 = 0, ef2 = 2;         long sum = ef1 + ef2;                // calculating sum of even Fibonacci value         while (ef2 <= limit)         {             // get next even value of Fibonacci sequence             long ef3 = 4 * ef2 + ef1;                    // If we go beyond limit, we break loop             if (ef3 > limit)                 break;                    // Move to next even number and update sum             ef1 = ef2;             ef2 = ef3;             sum += ef2;         }                return(int) sum;     }            // Driver code     public static void main (String[] args)      {         int limit = 400;         System.out.println(evenFibSum(limit));                } }    // This code is contributed by vt_m.

## Python3

 # Find the sum of all the even-valued  # terms in the Fibonacci sequence which  # do not exceed given limit.    # Returns sum of even Fibonacci numbers which # are less than or equal to given limit. def evenFibSum(limit) :     if (limit < 2) :         return 0        # Initialize first two even prime numbers     # and their sum     ef1 = 0     ef2 = 2     sm= ef1 + ef2            # calculating sum of even Fibonacci value     while (ef2 <= limit) :            # get next even value of Fibonacci          # sequence         ef3 = 4 * ef2 + ef1            # If we go beyond limit, we break loop         if (ef3 > limit) :             break            # Move to next even number and update         # sum         ef1 = ef2         ef2 = ef3         sm = sm + ef2            return sm    # Driver code limit = 400 print(evenFibSum(limit))    # This code is contributed by Nikita Tiwari.

## C#

 // C# program to Find the sum of all // the even-valued terms in the  // Fibonacci sequence which do not // exceed given limit.given limit. using System;    class GFG {            // Returns sum of even Fibonacci      // numbers which are less than or     // equal to given limit.     static int evenFibSum(int limit)     {         if (limit < 2)             return 0;                // Initialize first two even         // prime numbers and their sum         long ef1 = 0, ef2 = 2;         long sum = ef1 + ef2;                // calculating sum of even          // Fibonacci value         while (ef2 <= limit)         {                            // get next even value of              // Fibonacci sequence             long ef3 = 4 * ef2 + ef1;                    // If we go beyond limit,             // we break loop             if (ef3 > limit)                 break;                    // Move to next even number             // and update sum             ef1 = ef2;             ef2 = ef3;             sum += ef2;         }                return(int) sum;     }            // Driver code     public static void Main ()      {         int limit = 400;         Console.Write(evenFibSum(limit));                } }    // This code is contributed by Nitin Mittal.

## PHP

 \$limit)             break;            // Move to next even number         // and update sum         \$ef1 = \$ef2;         \$ef2 = \$ef3;         \$sum += \$ef2;     }        return \$sum; }    // Driver code \$limit = 400; echo(evenFibSum(\$limit));    // This code is contributed by Ajit. ?>

Output :

188

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