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Python Fibonacci Series program

How to Write Python Fibonacci Series program using While Loop, For Loop, and Recursion?. As per Mathematics, Python Fibonacci Series, or Fibonacci Numbers in Python are the numbers displayed in the following sequence. Fibonacci Series = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 …

If you observe the above Python Fibonacci series pattern, First Value is 0, Second Value is 1, and the following number is the result of the sum of the previous two numbers. For example, Third value is (0 + 1), Fourth value is (1 + 1) so on and so forth.

Python Fibonacci Series program Using While Loop

This Python program allows the user to enter any positive integer. Next, this program displays the Python Fibonacci series of numbers from 0 to user-specified numbers using Python While Loop.

# Python Fibonacci series Program using While Loop

# Fibonacci series will start at 0 and travel upto below number
Number = int(input("\nPlease Enter the Range Number: "))

# Initializing First and Second Values of a Series
i = 0
First_Value = 0
Second_Value = 1
           
# Find & Displaying Fibonacci series
while(i < Number):
           if(i <= 1):
                      Next = i
           else:
                      Next = First_Value + Second_Value
                      First_Value = Second_Value
                      Second_Value = Next
           print(Next)
           i = i + 1
Python Fibonacci Series Program using While Loop

This Python Fibonacci program allows the user to enter any positive integer and then, that number assigned to variable Number. Next, We declared three integer variables i, First_Value, and Second_Value and assigned values.

The below Python While Loop make sure that the loop starts from 0, and it is less than the user given number. Within the While loop of the Python Fibonacci series program, we used the If statement.

  • If i value is less than or equal to 1, then Next = i
  • If i value is greater than 1, perform calculations inside the Else block.
while(i < Number):
           if(i <= 1):
                      Next = i
           else:
                      Next = First_Value + Second_Value
                      First_Value = Second_Value
                      Second_Value = Next
           print(Next)
           i = i + 1

Let us see the working principle of this while loop in this Python Fibonacci Series example in the iteration wise. In this fibonacci series example, User Entered value: Number = 4 and i = 0, First_Value = 0, Second_Value = 1

Python While First Iteration

  • While (0 < 4) is TRUE. So, Fibonacci Series program starts executing statements inside the while loop.
  • Within the while loop, we have If statement and the condition if (0 <= 1) is TRUE. So, Next = 0 and compiler exit from if statement block.
  • Print statement print(Next) print the value 0.
  • Lastly, i incremented to 1.

Second Iteration

  • While (1 < 4) is TRUE. 
  • Within the while loop, we have Python If statement and the condition if (1 <= 1) is TRUE. So, Next = 1 and compiler exit from if statement block.
  • Print statement print(Next) print the value 1.
  • i incremented to 1.

Third Iteration

While (2 < 4) is TRUE in this Fibonacci series in python. Within the while loop, we have If statement and the condition if (2 <= 1) is FALSE, so statements inside the else block to start executing.

Next = First_Value + Second_Value

Next = 0 + 1 = 1

First_Value = Second_Value = 1

Second_Value = Next = 1

Next, Print statement print(Next) print the value 1. Lastly, i incremented to 1

Fourth Iteration: while (3 < 4) is TRUE. So, the Python program starts executing statements inside the while loop.

The condition if (3 <= 1) is FALSE, so statements inside the else block to start executing.

Next = First_Value + Second_Value

Next = 1 + 1 = 2

First_Value = Second_Value = 1

Second_Value = Next = 2

Next, Print statement print(Next) print the value 2. Lastly, i incremented to 1

Fifth Iteration

While (4 < 4) is FALSE so, it exits from the while loop.

From the above, Our final output of Next values are: 0 1 1 2

Fibonacci Series program Using For Loop

This Python Fibonacci Series using for loop example allows the user to enter any positive integer. Next, this program displays the Fibonacci series of numbers from 0 to user-specified numbers using Python For Loop.

# Python Fibonacci series Program using For Loop

# Fibonacci series will start at 0 and travel upto below number
Number = int(input("\nPlease Enter the Range Number: "))

# Initializing First and Second Values of a Series
First_Value = 0
Second_Value = 1
           
# Find & Displaying Fibonacci series
for Num in range(0, Number):
           if(Num <= 1):
                      Next = Num
           else:
                      Next = First_Value + Second_Value
                      First_Value = Second_Value
                      Second_Value = Next
           print(Next)
Python Fibonacci Series Program using For Loop

Python Fibonacci Series program Using Recursion

This Fibonacci Series program allows the user to enter any positive integer. Then this program displays the Fibonacci series of numbers from 0 to user given number using Recursion concept.

# Python Fibonacci series Program using Recursion

# Recursive Function Beginning
def Fibonacci_series(Number):
           if(Number == 0):
                      return 0
           elif(Number == 1):
                      return 1
           else:
                      return (Fibonacci_series(Number - 2)+ Fibonacci_series(Number - 1))

# End of the Function

# Fibonacci series will start at 0 and travel upto below number
Number = int(input("\nPlease Enter the Range Number: "))

# Find & Displaying Fibonacci series
for Num in range(0, Number):
           print(Fibonacci_series(Num))
Python Fibonacci Series Program using Recursion

In this Python Fibonacci Series program example, we defined a function. The following function accept integer values as parameter value and return value.

def Fibonacci_series(Number):

Let’s see the Elif statement inside the above-specified functions

  • if (Number == 0) check whether the given number is 0 or not. If it is TRUE, the function returns the value Zero.
  • if(Number == 1) check whether the given number is 1 or not. If it is TRUE, function return the value One.
  • And, if the number is greater than 1, the statements inside the else block executed.

Within the Else block of this Python Fibonacci series, we called the function recursively to display the Fibonacci series.

return (Fibonacci_series(Number - 2)+ Fibonacci_series(Number - 1))

For the demonstration of fibonacci series, Number = 2

(Fibonacci_series(Number – 2)+ Fibonacci_series(Number – 1))

(Fibonacci_series(2 – 2)+ Fibonacci_series(2 – 1))

It means, (Fibonacci_series(0)+ Fibonacci_series(1))

return (0 + 1) = return 1

NOTE: For Recursive functions, it is very important to place a condition before using the function recursively. Otherwise, we end up in infinite execution (Same like infinite Loop).