Fibonacci Series Program in Python

What is the Fibonacci series

The Fibonacci series is a sequence where each number is the sum of the two before it. It starts 0, 1, then continues 1, 2, 3, 5, 8, 13.... It is a favourite programming exercise and a beautiful pattern found in nature too.

Fibonacci with a loop

n = 8
a, b = 0, 1
for i in range(n):
    print(a, end=" ")
    a, b = b, a + b

We keep two numbers, a and b. Each round we print a, then update both so they move forward through the sequence.

Dry run

How a, b = b, a+b works

This one line is the heart of the program. Python first works out the whole right side using the current values, then assigns both variables together:

a, b = b, a + b
# right side uses OLD a and b
# then a = old b, b = old a + old b

Because both are updated at once, you do not need a temporary variable to hold the old value — Python handles it for you.

Fibonacci with recursion

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

for i in range(8):
    print(fib(i), end=" ")

This mirrors the maths: fib(n) = fib(n-1) + fib(n-2), with base cases fib(0)=0 and fib(1)=1. It is elegant but slow for large n — use the loop for big series.

Common mistakes

• Wrong starting values. Begin with a, b = 0, 1, or the whole series shifts.
• Updating a and b separately. Do a, b = b, a+b in one line, or the second update uses the new a.
• Deep recursion for big n. Plain recursion is very slow — prefer the loop.
• Missing the base case in recursion. Without if n <= 1, it never stops.

Summary

• Fibonacci: each number is the sum of the previous two, starting 0, 1.
• The loop keeps two numbers and prints them in turn.
• a, b = b, a+b updates both at once — no temp variable.
• Recursion mirrors the maths but is slow for large n.
• Use the loop for printing long series.

Next, try the factorial program, or practise Python loops.