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NJOKU SAMSON EBERE

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# Algorithm 101: 3 Ways to Get the Fibonacci Sequence

In mathematics, the Fibonacci numbers, commonly denoted Fn, form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. - Wikipedia

In this article, we don't want to just return the `nth term` of a sequence, but we want to return the whole sequence as an `array` depending on the `starting points` given. Our counting follows the image below:

``````
fibonacci(8); // 21

``````

We are already used to the function call above usually achieved by the code below:

``````
function fibonacci(n) {
let firstNum = 0;
let secondNum = 1;
let sum = 0;

for (let i = 0; i <= n - 2; i++) {
sum = firstNum + secondNum;
firstNum = secondNum;
secondNum = sum;
}

return sum;
}

``````

Now, we want to move a little further to returning the whole sequence depending on the starting points (array of 2 numbers) and the limit (nth term) given.

``````
fibonacciSequence([0, 1], 9); //[ 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ]

fibonacciSequence([10, 20], 9); //[ 10, 20, 30, 50, 80, 130, 210, 340, 550, 890 ]

``````

### Prerequisite

To benefit from this article, you need to possess basic understanding of javascript's arithmetic and array methods.

### Let's do this!

• for...loop
``````      function fibonacciSequence(array, limit) {
let finalArray = [...array];

for (let i = 0; i < limit - 1; i++) {
let sum = array + array;
finalArray.push(sum);
array = [array, sum];
}

return finalArray;
}
``````
• while...loop
``````      function fibonacciSequence(array, limit) {
let finalArray = [...array];
let counter = 0;

while (counter < limit - 1) {
let sum = array + array;
finalArray.push(sum);
array = [array, sum];
counter++;
}

return finalArray;
}
``````
• do...while...loop
``````      function fibonacciSequence(array, limit) {
let finalArray = [...array];
let counter = 0;

do {
let sum = array + array;
finalArray.push(sum);
array = [array, sum];
counter++;
} while (counter < limit - 1);

return finalArray;
}
``````

### Conclusion

There are many ways to solve problems programmatically. I will love to know other ways you solved yours in the comment section.

If you have questions, comments or suggestions, please drop them in the comment section.

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