Difference between revisions of "Fibonacci Sequence"

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Fibonacci Sequence is defined as the sequence of numbers in which each number in the sequence is equal to the  sum of two numbers before it.
Fibonacci Sequence is defined as the sequence of numbers in which each number in the sequence is equal to the  sum of two numbers before it.


Fibonacci sequence is given as <math>0,1,1,2,3,5,8,13,21,34,55.........</math>
Fibonacci sequence is given as <math>0,1,1,2,3,5,8,13.........</math>


Here the first two terms are <math>0,1</math>
Here the first two terms are <math>0,1</math>
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== Fibonacci Sequence Formula ==
== Fibonacci Sequence Formula ==
The Fibonacci sequence of numbers <math>F_n</math> is defined using the recursive relation with the seed values <math>F_0=0</math> and <math>F_1=1</math>
<math>F_n=F_{n-1}+F_{n-2}</math>
Here, the sequence is defined using two different parts, such as kick-off and recursive relation.
<math>F_0=0</math> and <math>F_1=1</math> is the the kick-off part
<math>F_n=F_{n-1}+F_{n-2}</math> is the recursive relation part
The  sequence starts with 0 rather than 1.
== Fibonacci Sequence List ==
The List of first 10 terms in the Fibonacci Sequence  is
{| class="wikitable"
|+
|<math>0,1,1,2,3,5,8,13,21,34.....</math>
|}
The list of Fibonacci numbers are calculated as shown below
{| class="wikitable"
|+
!<math>F_n</math>
!<math>F_n=F_{n-1}+F_{n-2}</math>
!<math>Fibonacci \  Number</math>
|-
|<math>F_0</math>
| -
|<math>0</math>
|-
|<math>F_1</math>
| -
|<math>1</math>
|-
|<math>F_2</math>
!<math>F_2=F_1+F_0</math>
|<math>1</math>
|-
|<math>F_3</math>
!<math>F_3=F_2+F_1 </math>
|<math>2</math>
|-
|<math>F_4</math>
!<math>F_4=F_3+F_2</math>
|<math>3</math>
|-
|<math>F_5</math>
!<math>F_5=F_4 +F_3</math>
|<math>5</math>
|-
|<math>F_6</math>
!<math>F_6=F_5 +F_4</math>
|<math>8</math>
|-
|<math>F_7</math>
!<math>F_7=F_6 +F_5</math>
|<math>13</math>
|-
|<math>F_8</math>
!<math>F_8=F_7 +F_6</math>
|<math>21</math>
|}

Revision as of 13:42, 18 October 2023

Fibonacci Sequence was discovered by Italian Mathematician Leonardo Fibonacci (1170-1250) is a sequence of numbers starting with zero and one , is a steadily increasing series where each number is equal to the sum of the preceding two numbers.

Definition

Fibonacci Sequence is defined as the sequence of numbers in which each number in the sequence is equal to the sum of two numbers before it.

Fibonacci sequence is given as

Here the first two terms are

The third term is obtained by adding the first and second term

The fourth term is obtained by adding the second and third term

The fourth term is obtained by adding the third term and fourth term and so on.

Fibonacci Sequence Formula

The Fibonacci sequence of numbers is defined using the recursive relation with the seed values and

Here, the sequence is defined using two different parts, such as kick-off and recursive relation.

and is the the kick-off part

is the recursive relation part

The sequence starts with 0 rather than 1.

Fibonacci Sequence List

The List of first 10 terms in the Fibonacci Sequence is

The list of Fibonacci numbers are calculated as shown below

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-