In today’s lesson, we are going to learn a Python Program to Find the Fibonacci Series Using a While Loop.

## What is Fibonacci series in Python?

In Python, the Fibonacci series is a sequence of numbers in which each number is the sum of the two preceding ones, often beginning with 0 and 1. It is described mathematically by the recurrence relation F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.

The Fibonacci series can be created in Python using a variety of approaches such as recursion, iteration, or memoization. One frequent way is to iteratively calculate and store the Fibonacci numbers using a loop. Because of its intriguing mathematical features and self-replicating patterns, this series has applications in many domains, including mathematics, computer science, and nature, and it frequently arises in algorithms, number theory, and dynamic programming issues.

**Python Program to Find the Fibonacci Series Using While Loop**

# Find Fibonacci Series in Python Using While Loop # we are taking a number from user as input # entered value will be converted to int from string n = int(input("Number of Fibonacci Series to be Printed: ")) # print initial 2 number to start fibonacci series a, b = 0, 1 print(a, b, end=' ') i = 0 while (i < n-2): c = a + b # add the last two numbers and print print(c, end=' ') a = b b = c i = i + 1

**Input from the user**- As the Fibonacci series is a non terminating series, we ask the user to enter the number, which will be the length of the Fibonacci series to be printed
- As we asking the user to enter a number, we use the int() function to convert the user’s input into an integer and stored as ‘n’
- Syntax : n = int(input(“Number of Fibonacci Series to be Printed: “))

**Initiating the Series**- As we know that the first 2 digits of the Fibonacci Series is 0 and 1, we are going to assign them a variable ‘a’ and ‘b’ respectively
- These value are then printed using the print() function with ‘end=’ ‘’ to ensure the value are printed on the same line

**Initiating the While loop**- As we need multiple iteration of the same operation, we are using the while loop to perform this action
- We are using variable ‘i’ to keep track of the number of iterations
- The ‘while’ loop is run for ‘n-2’ times, as the first two digits are defined already
- Inside the loop, the next number in the sequence is calculated as the sum of the previous two numbers, ‘a’ and ‘b’. This value is stored in the variable ‘c’
- The ‘print()’ function is used to print ‘c’ on the same line as the previous values separated by a space

**Iteration and Termination of the While Loop**- The values of ‘a’ and ‘b’ are updated for the next iteration
- With ‘a’ set to the previous value of ‘b’
- And ‘b’ being the previous value of ‘c’
- Finally, the loop counter ‘i’ is raised by 1, and the loop continues till the counter reached ‘n-2’

The code exists giving out the sequence in a line

#### Output:

```
Number of Fibonacci Series to be Printed: 10
0 1 1 2 3 5 8 13 21 34
```

In this program, we generated the Fibonacci series using a while loop. When the user enters the number of terms of the series to be printed, say ‘n’. The code outputs the first two terms in the series, which are initialised as 0 and 1, respectively. Then it starts a while loop, which runs until it prints the ‘n-2′ number of terms. Within the loop, the program adds the series’ last two values (a and b) to get the next term (c), which is then printed.

The values of ‘a’ and ‘b’ are shifted to the right by one position, making ‘b’ the current term and ‘a’ the previous term, and the loop continues like before.

The output of the program is the Fibonacci series, when the user enters ’10’ is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34.

**Why do **we use the **While loop to find the Fibonacci series**

Apart from the above method, you can also find the Fibonacci series using recursion or for loop in Python. If the size of the input is large, using recursion can lead to excessive stack usage and slow execution time but, for small input values, recursion can be an elegant and concise solution. When we use a while loop, as shown above, the coding is simple and efficiently generates the series.

In this tutorial, we learned about the Fibonacci series and a Python Program to find the Fibonacci Series using the while loop. We ask the user to define the length of the series, as the series is a never-ending series.

**FAQs for Fibonacci series by using While loop**

**Can I modify the above code to print the Fibonacci series in reverse order?**

Yes, you can modify the code by changing the initial values of ‘a’ and ‘b’ to the last two numbers of the series., Then apply a decrementing loop variable ‘i’ instead of incrementing it.

**How can I optimize the above code to use fewer variables?**

You can use a single variable to store the sum of the last two numbers instead of ‘c’. This will reduce the number of variables used in the code.

**Can I generate the Fibonacci series starting from any two given numbers?**

Yes, you can modify the code by changing the initial values of ‘a’ and ‘b’ to the desired numbers.

**What will happen if I enter a negative number for the number of terms in the Fibonacci series?**

The code will result in an error message. However, you can add a check at the beginning of the code to ensure that the input value is non-negative.

**What are some real-world applications of the Fibonacci series?**

The Fibonacci series has applications in many fields, including finance, computer science, and nature. It can be used to model population growth, stock market trends, and the growth of plants.