freeCodeCamp/guide/english/certifications/coding-interview-prep/project-euler/problem-2-even-fibonacci-nu.../index.md

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2018-10-12 19:37:13 +00:00
---
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)