Q: Is 21 a Fibonacci Number?

How is 21 a Fibonacci number?

The Fibonacci Sequence is a series of numbers where you add the previous two numbers together. The sum of each is a Fibonacci number.

You start with 0 and add 1 to get the answer 1. You then add 1 + 1 to get 2. Then 2 + 1 to get 3. Then 2 + 3 to get 5, and so on.

To help you see it a little better, the numbers you add together have been color coded:

0 + 1 = 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13

What would be the next Fibonacci number? If you answered 21, you're right. Here's how: You add 8 + 13, which equals 21. The sum of each set of numbers is a Fibonacci number. There are an infinite number of Fibonacci numbers.

So now that we have a little background on what a Fibonacci number is, let's work through it and try to see if 21 is a Fibonacci number.

Remember, we start with 0 + 1 = 1 then 1 + 1 = 2 then 1 + 2 = 3 then 2 + 3 = 5, and so on...

Long Form Fibonacci Test

0 + 1 = 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
13 + 21 = 34

Notice the green equation above. This shows that 21 IS a Fibonacci number.

• This is just one way to find a Fibonacci number and is arguably the easiest to understand. There are many ways to calculate a Fibonacci number. Take a look at Wikipedia for more information.

More Examples

Are any of the surrounding numbers a Fibonacci number?

Let's take a look and see...