Fibonacci Sequence in Mathematics

Fibonacci numbers form the Fibonacci sequence. These numbers are represented as the positive numbers which are formed in a sequential form. The numbers in the sequence come in a re-occurrence manner. Series which belong to the Fibonacci sequence will be – 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on. 

A Fibonacci number is the following number which is a result of adding the two previous numbers. For example: if the first two numbers in a series are 6 and 7 then the following number after this will be 13 (this is 6 + 7). In this manner, we get the Fibonacci series. 

In mathematics, the Fibonacci series list can be listed down. 

The Fibonacci Series list will be in a sequential manner. If a Fibonacci series trend is observed then you will notice that every third number in the data is actually the sum of the preceding two numbers. 

Also, in the next section, we are going to focus on what the Fibonacci series is and the formula to calculate the series. 

What is the Fibonacci Series?

Fibonacci series is a representation of Fibonacci sequential numbers, here in this data, every number is the sum of the previous two of its numbers. Also, to note in some data, 0 is often deleted as it eventually does not have any such effect, it will be a mere repetition of the same 2nd number. 

The Fibonacci Series is Named After Whom?

The Fibonacci Series is named after Leonardo Pisano Bogollo, he was an Italian Mathematician. The series was first named as this Italian Mathematician, later it was named as ‘Fibonacci’. The numbers in the series are denoted by Finn. As already discussed, Fibonacci numbers are the repetition of the sum of the two preceding numbers. 

You might wonder about the use of learning the Fibonacci numbers, will yes! There are some definitive examples where Fibonacci numbers are used in the real life. These numbers are found in the biological environment only. The tree’s branches, the patterns of the flower petals all represent the Fibonacci sets or series of numbers.  Fibonacci numbers can be as follows: 3, 6, 9, 15, 24, and so on. 

So, given the first number as 3 can be written as F3 and the second number as 6 can be written as S6, so now adding the series we get the third number which is T9. 

Likewise, F6 + S9 = T15 … and so on. 

What Will Be The Formula For Fibonacci Numbers? 

In the study of Mathematics, the Fibonacci series formula can be used if there are any missing numbers, we can help with this formula. The missing terms in the Fibonacci Series are thus, estimated out with the help of the following formula – n + 1st term which is in a sequence of the recurring formula. 

Where is the Fibonacci Sequence Used?

The Fibonacci sequence is applied in the following fields:

  • In nature, like gardening Fibonacci Series are used.
  • In musical chords, the Fibonacci Series is used.
  • In studying the human body this series is studied. 
  • In coding languages of the computer, Fibonacci Series is used.
  • In Physical Science, Quantum Physics, Quantum Mechanics, and Cryptography even the Fibonacci series is used. 

Thus, we see the Fibonacci series is indeed useful in various fields of study. 

As we come to the end of the discussion, the students are advised to practice more of these series, to know more about this feel free to visit Cuemath for a detailed understanding. Head on to our page and explore your learning in the Mathematics field.