**What is Fibonacci series?**

A Fibonacci series is a sequence of numbers where each number is a sum of previous 2 numbers. First two terms of a Fibonacci series are 0 and 1.

**Method 1: Iterative Approach**

This approach is based on the following algorithm

1. Declare two variables representing two terms of the series. Initialize them to 0 and 1 as the first and second terms of the series respectively.

2. Initialize a variable representing loop counter to 0.

3. Loop from 0 to the total number of terms in the series.

4. In every iteration,

A. add the variables defined in step 1. This represents a term(or item) of the Fibonacci series.

B. assign the value of second variable to first and the sum in above step A to the second variable.

Python program to generate fibonacci series written as per the above algorithm follows.

# read the total number of items in Fibonacci series max_item_input = input("Enter the number of items in Fibonacci series\n") max_item = int(max_item_input) # variables to hold two items of series first = 0 second = 1 # loop counter item = 0 # iterate till the total number of items in the series while item < max_item: # add two terms, the result represents the subsequent element of the series sum = first + second # print current item print(first,end = ",") # assign variables first = second second = sum # increment loop counter item += 1 |

Enter the number of items in Fibonacci series

6

0,1,1,2,3,5,

**Method 2: Using recursion**

Create a recursive function which receives an integer as argument. This

*integer argument represents the position in Fibonacci series*and returns the value at that position. Thus, if it receives 5, it returns the value at 5th position in Fibonacci series.

This recursive function returns 0 and 1 if the argument value is 0 or 1. For all other values it calls itself with the sum of nth and (n-1)th positions.

The program reads the total number of elements in Fibonacci series from keyboard. It then initiates a loop starting from 0 till this input value. In every iteration, the recursive function is called and the resultant Fibonacci item for that position is printed.

def fibonacci(number): # return 0 and 1 for first and second terms if number == 0: return 0 elif number == 1: return 1 else: # return the sum of two numbers return fibonacci(number - 1) + fibonacci(number - 2) # read the total number of items in Fibonacci series max_item_input = input("Enter the number of items in Fibonacci series\n") max_item = int(max_item_input) # iterate from 0 till number of terms for count in range(max_item): print(fibonacci(count), end=",") |

Output of above execution is

Enter the number of items in Fibonacci series

8

0,1,1,2,3,5,8,13,

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