**Fibonacci sequence:**

The Fibonacci sequence is a sequence type in which the sum of the previous two numbers is each consecutive number.

First few Fibonacci numbers are 0 1 1 2 3 5 8 …..etc.

## Fibonacci sequence without recursion:

Let us now write code to display this sequence without recursion. Because recursion is simple, i.e. just use the concept,

Fib(i) = Fib(i-1) + Fib(i-2)

However, because of the repeated calculations in recursion, large numbers take a long time.

So, without recursion, let’s do it.

**Approach:**

- Create two variables to hold the values of the previous and second previous numbers.
- Set both variables to 0 to begin.
- Begin a loop until N is reached, and for each i-th index
- Print the sum of the previous and second most previous i.e sum= previous + second previous
- Assign previous to second previous i.e. second previous= previous
- Assign sum to previous i.e previous=sum

**Below is the implementation:**

**1)C++ implementation of above approach.**

#include <iostream> using namespace std; int main() { // given number int n = 10; // initializing previous and second previous to 0 int previous = 0; int secondprevious = 0; int i; // loop till n for (i = 0; i < n; i++) { // initializing sum to previous + second previous int sum = previous + secondprevious; cout << sum << " "; if (!sum) previous = 1; secondprevious = previous; previous = sum; } return 0; }

**2)Python implementation of above approach.**

# given number n = 10 # initializing previous and second previous to 0 previous = 0 secondprevious = 0 # loop till n for i in range(n): sum = previous + secondprevious print(sum, end=" ") if (not sum): previous = 1 # initializing value to previous to second previous secondprevious = previous previous = sum

**Output:**

0 1 1 2 3 5 8 13 21 34

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