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The Fibonacci sequence is a series of integers where each number is the sum of the preceeding two numbers, and the first two numbers in the series is 0 and 1. The first 10 numbers in the series are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34.

Some definitions start the series at 1 and 1, omitting the 0.

The ratio of two sequential Fibonacci numbers, as the numbers get large, approaches phi, which is the golden mean, (1 + sqrt(5)) / 2, or about 1.61803. There are many, many other uses, as well as observations of the sequence in nature.

Fibonacci numbers get large very quickly, so generating more than a few of them requires an arbitrary decimal math library. In particular, the 47th number in the sequence is 2,971,215,073, which is the largest Fibonacci number that can be stored in a 32-bit unsigned binary integer, and the 93rd term is 12,200,160,415,121,876,738, which is the largest possible in 64-bit.

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Q: How does the Fibonacci sequence work?
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Related questions

Why does Fibonacci sequence work?

Work for what?


When did Fibonacci discover the Fibonacci sequence?

Leonardo Fibonacci discovered the Fibonacci sequence In the 12th century.


Why is the Fibonacci sequence named after Fibonacci?

Leonardo Fibonacci discovered the number sequence which is named after him.


What are the ninth and tenth numbers in the Fibonacci sequence?

The 9th number in the Fibonacci Sequence is 34, and the 10th number in the Fibonacci sequence is 89.


Why did Fibonacci think of the Fibonacci code?

There is the Fibonacci sequence but what is the Fibonacci code?


Who was Leonardo Fibonacci?

Leonardo Fibonacci was the father and creator of the fibonacci sequence a very famous mathematic sequence


Why did Fibonacci create the Fibonacci Sequence?

Leonardo Fibonacci did not create the Fibonacci Sequence -- he discovered it during his studies as a mathematician.


How did Fibonacci get his idea for the Fibonacci Sequence?

The Fibonacci Sequence itself was not CREATED by Leonardo of Pisa (more commonly known as Leonardo Fibonacci or simply Fibonacci). He is credited to the introduction of the sequence to the western world, (Hence the name "The Fibonacci Sequence"); however origins of the Fibonacci can be traced back to 200BC. *TJB*


What is the 20th Fibonacci number in the sequence?

The 20th Fibonacci number in the sequence is 6,765.


What is the 16th number of the Fibonacci sequence?

The 16th number of the Fibonacci sequence is 987.


What is a Fibonacci sequence using 84?

The Fibonacci sequence requires two numbers as "seeds".


What is the Fibonacci sequence used for?

The Fibonacci sequence is used for many calculations in regards to nature. The Fibonacci sequence can help you determine the growth of buds on trees or the growth rate of a starfish.


How do you get the Fibonacci sequence?

Start with 1 and 2. Then each number in the Fibonacci sequence is the sum of the previous two numbers in the sequence.


What is the Fibonacci sequence of twenty-two?

The Fibonacci sequence requires two initial numbers to be specified.


How old was Fibonacci when he discovered the Fibonacci sequence?

42


Is the Fibonacci Sequence named after Leonardo Fibonacci?

Yes.


How would one describe a Fibonacci number?

A Fibonacci number, Fibonacci sequence or Fibonacci series are a mathematical term which follow a integer sequence. The first two numbers in Fibonacci sequence start with a 0 and 1 and each subsequent number is the sum of the previous two.


Who pioneered the finonacci sequence?

Not sure about the finonacci sequence but the Fibonacci sequence was discovered and studies by Fibonacci, also known as Leonardo of Pisa.


What is the 24th Fibonacci number?

Assuming the Fibonacci sequence starts with the numbers 0, 1, as per sequence A000045, the 24th Fibonacci number is 28657.


Is The Fibonacci sequence arithmetic?

No, the Fibonacci sequence is not an arithmetic because the difference between consecutive terms is not constant


How do you get 1123 in Fibonacci?

1123 is not a number included in the Fibonacci Sequence.


When did Fibonacci make the Fibonacci number sequence?

middle ages


Who was fibanacci?

Fibonacci was an Italian scientist who created the Fibonacci sequence


Who found the Fibonacci sequence?

Leonardo Fibonacci, or Leonardo of Pisa.


Where was the Fibonacci series made?

The Fibonacci sequence is named after Leonardo of Pisa, who was known as Fibonacci. Fibonacci's 1202 book Liber Abaciintroduced the sequence to Western European mathematics, although the sequence had been previously described in Indian mathematics.