Q: Is 109,714,889 a Fibonacci Number?

How is 109,714,889 not 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 109,714,889 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
21 + 34 = 55
34 + 55 = 89
55 + 89 = 144
89 + 144 = 233
144 + 233 = 377
233 + 377 = 610
377 + 610 = 987
610 + 987 = 1,597
987 + 1,597 = 2,584
1,597 + 2,584 = 4,181
2,584 + 4,181 = 6,765
4,181 + 6,765 = 10,946
6,765 + 10,946 = 17,711
10,946 + 17,711 = 28,657
17,711 + 28,657 = 46,368
28,657 + 46,368 = 75,025
46,368 + 75,025 = 121,393
75,025 + 121,393 = 196,418
121,393 + 196,418 = 317,811
196,418 + 317,811 = 514,229
317,811 + 514,229 = 832,040
514,229 + 832,040 = 1,346,269
832,040 + 1,346,269 = 2,178,309
1,346,269 + 2,178,309 = 3,524,578
2,178,309 + 3,524,578 = 5,702,887
3,524,578 + 5,702,887 = 9,227,465
5,702,887 + 9,227,465 = 14,930,352
9,227,465 + 14,930,352 = 24,157,817
14,930,352 + 24,157,817 = 39,088,169
24,157,817 + 39,088,169 = 63,245,986
39,088,169 + 63,245,986 = 102,334,155
63,245,986 + 102,334,155 = 165,580,141

Notice the last equation above (in red). This shows that 109,714,889 is NOT a Fibonacci number because the sum of the last equation is larger than the number 109,714,889 and the sum of the equation before it is smaller than the number 109,714,889.

• 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

Here are the next few Fibonacci numbers for you to take a look at:

165,580,141 267,914,296 433,494,437 701,408,733

Are any of the surrounding numbers a Fibonacci number?

Let's take a look and see...