The [**Fibonacci Sequence**](https://www.educative.io/answers/what-is-the-fibonacci-sequence) is the series of numbers:

 $0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...$  

 The series starts with $0$ and $1$ as the first two numbers in the series. The next number in the series is found by summing the two numbers before it.

For example:
- The third number in the sequence, $1$, is found by adding the two numbers before it $(0+1)$.
- The fourth number in the sequence, $2$, is found by adding the two numbers before it $(1+1)$.


# Implementing the Fibonacci Sequence
Fibonacci Sequence can be implemented both iteratively and recursively in Python.

 For both examples, try changing the value of the argument passed to the function to print out more numbers in the sequence.

## Iterative implementation

def fib(number_of_terms):
   counter = 0

   first = 0
   second = 1
   temp = 0
 
   while counter <= number_of_terms:
      print(first)
      temp = first + second
      first = second
      second = temp
      counter = counter + 1

# Driver Code
fib(10)

In the above implementation, The code prints the `first` value on each iteration of the loop. Each iteration calculates the next value by summing the previous two values and then updates the values of `first` and `second`. The time complexity of the above iterative implementation is $O(n)$.



def fib(term):
   if term <= 1:
       return (term)
   else:
       return (fib(term-1) + fib(term-2))

# Change this value to adjust the number of terms in the sequence.
number_of_terms = 10
for i in range(number_of_terms):
    print(fib(i))


The above program computes the Fibonacci value by calling itself with a lesser value several times. The termination condition for this is reached when `term == 0` and `term == 1`. The time complexity for this solution is $O(2^n)$.

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How to implement the Fibonacci sequence in Python

The Fibonacci Sequence is the series of numbers: 0,1,1,2,3,5,8,13,21,34,...0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...0,1,1,2,3,5,8,13,21,34,... The series starts with 000 and 111 as the first two numbers in the series. The next number in the series is found by summing the two numbers before it. For example:  The third number in the sequence, 111, is found by adding the two numbers before it (0+1)(0+1)(0+1). The fourth number in the sequence, 222, is found by adding the two numbers before it (1+1)(1+1)(1+1).  

How to implement the Fibonacci sequence in Python

Implementing the Fibonacci Sequence

Iterative implementation

Recursive Implementation