JavaScript Program to Find n-th Fibonacci Number

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. The sequence goes as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. Given an integer n, the task is to find the n-th Fibonacci number.

These are the following methods:

Recursive Approach

In this method, the Fibonacci number is determined by a recursive function. Though straightforward, this method may be ineffective if repeated function calls are made.

Example: This example shows the recursive approach to find the nth term.

Javascript

function fibonacciRecursive(n) {
    if (n <= 1)
        return n;
    return fibonacciRecursive(n - 1) +
        fibonacciRecursive(n - 2);
}

const n = 12;
console.log(`The ${n}-th Fibonacci number is
: ${fibonacciRecursive(n)}`);

Output

The 12-th Fibonacci number is
: 144

Iterative Approach

We compute the Fibonacci number sequentially using a loop. Due to the elimination of pointless function calls, it is more efficient than the recursive method.

Example: This example shows the Iterative approach to finding the nth term.

Javascript

function fibonacciIterative(n) {
    let fib = [0, 1];
    for (let i = 2; i <= n; i++) {
        fib[i] = fib[i - 1] + fib[i - 2];
    }
    return fib[n];
}

const n = 12;
console.log(`The ${n}-th Fibonacci number is:
 ${fibonacciIterative(n)}`);

Output

The 12-th Fibonacci number is:
 144

Dynamic Programming Approach

We prevent unnecessary calculations by storing previously computed Fibonacci numbers in an array, which increases algorithmic performance.

Example: This example shows the Iterative approach to finding the nth term.

Javascript

function fibonacciDynamic(n) {
    let fib = [0, 1];
    for (let i = 2; i <= n; i++) {
        fib[i] = fib[i - 1] + fib[i - 2];
    }
    return fib[n];
}

const n = 2;
console.log(`The ${n}-th Fibonacci number is:
 ${fibonacciDynamic(n)}`);

Output

The 2-th Fibonacci number is:
 1

Conclusion

We have discussed three methods that you may use in JavaScript to find the n-th Fibonacci number. Iterative and dynamic programming methodologies are more efficient than the recursive approach, which is simpler but less effective.