Fibonacci Series In Python Using For Loop’

The Fibonacci series is a sequence of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. The sequence goes as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. This series is not only intriguing due to its inherent mathematical properties but also widely used in various fields such as mathematics, computer science, and nature.

Mathematical Logic

The Fibonacci series follows a simple mathematical logic. The first two numbers in the sequence are 0 and 1. From the third number onward, each number is the sum of the two preceding ones. Mathematically, it can be expressed as:

Syntax :

F(n)=F(n−1)+F(n−2)

where F(n) is the nth number in the Fibonacci sequence.

Fibonacci Series In Python Using For Loop

Below, are the ways to create Fibonacci Series In Python Using For Loop.

• Using a List
• Using Variables
• Using Generator Function

Fibonacci Series In Python Using a List

In below, the function uses a list to store the Fibonacci numbers. It starts with the initial values [0, 1] and iterates through the range from 2 to n, calculating each Fibonacci number and appending it to the list.

Python3

def fibonacci_with_list(n):
    fib_series = [0, 1]
    for i in range(2, n):
        fib_series.append(fib_series[-1] + fib_series[-2])
    return fib_series

# Example usage:
n = 10
result = fibonacci_with_list(n)
print(f"Fibonacci series with {n} elements:", result)

Output

Fibonacci series with 10 elements: [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]

Fibonacci Series In Python Using Variables

In this example, below function uses two variables, a and b, to store the last two numbers in the Fibonacci sequence. It iterates through the range from 0 to n, updating the variables in each iteration and printing the current Fibonacci number.

Python3

def fibonacci_with_variables(n):
    a, b = 0, 1
    for _ in range(n):
        print(a, end=" ")
        a, b = b, a + b

# Example usage:
n = 10
print(f"Fibonacci series with {n} elements:", end=" ")
fibonacci_with_variables(n)

Output

Fibonacci series with 10 elements: 0 1 1 2 3 5 8 13 21 34 

Fibonacci Series In Python Using Generator Function

In this example, below function uses a generator to yield Fibonacci numbers one at a time. It has similar logic to the previous example but is designed to be more memory-efficient, especially for large values of n.

Python3

def fibonacci_generator(n):
    a, b = 0, 1
    for _ in range(n):
        yield a
        a, b = b, a + b

# Example usage:
n = 10
result = list(fibonacci_generator(n))
print(f"Fibonacci series with {n} elements:", result)

Output

Fibonacci series with 10 elements: [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]

Conclusion

In this article, we explored the Fibonacci series and its mathematical logic. We then implemented various methods to generate the Fibonacci series in Python using a for loop. Whether using a list, variables, or a generator, the for loop proves to be a versatile tool for efficiently computing the Fibonacci sequence