---
title: Even Fibonacci Numbers
---
## Problem 2: Even Fibonacci Numbers

### Method:
- A fibonacci sequence is a sequence where `fib(n) = fib(n-1) + fib(n-1)`.
- In this challenge we have to sum all the even numbers upto `nth` term in the sequence.
- Example for `fiboEvenSum(10)`:
  + The sequence till 10th term is:
  1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144

  + Sum of all even number in the above sequence is:
  2 + 8 + 34 + 144 = 188

### Solution:

#### Basic Solution - Iterative:
```js
function fiboEvenSum(n) {
  let first = 1, second = 2, sum = 2, fibNum; // declaring and initializing variables
  if (n <= 1) return sum; // edge case
  for (let i = 2; i <= n; i++){  // looping till n
    fibNum = first + second;    // getting the ith fibonacci number
    first = second;
    second = fibNum;
    if (fibNum%2 == 0) sum+=fibNum;  // If even add to the sum variable
  }
  return sum;
}
```
#### Advanced Solution - Recursive:
```js
// We use memoization technique to save ith fibonacci number to the fib array 
function fiboEvenSum(n){
  const fib = [1, 2]; 
  let sumEven = fib[1];
  function fibonacci(n){
    if (n <= 1) return fib[n]; // base condition
    else if (fib[n]) return fib[n]; // if the number exists in the array we cache it and return
    else {
      fib[n] = fibonacci(n-1) + fibonacci(n-2); // otherwise calculcate and save it to the array
      if (fib[n]%2 == 0) sumEven+=fib[n];  //if the number is even, add it to the sumEven variable
      return fib[n];
    }
  }
  fibonacci(n); // run the recursive function
  return sumEven;
}
```
- [Run Code](https://repl.it/@ezioda004/Project-Euler-Problem-2-Even-Fibonacci-Numbers)
### References:
- [Wikipedia](https://en.wikipedia.org/wiki/Fibonacci_number)