Contents

## Nth Fibonacci Number

To find the Nth Fibonacci number, we can use Recursion technique or a For Loop.

In this tutorial, we will write Python programs that cover both of the above said techniques to find out Nth Fibonacci number.

## 1. Nth Fibonacci Number using Recursion

In the following program, we write a function fibonacci() that can take n as argument, and return the nth Fibonacci number. This fibonacci() is a recursion function.

**Algorithm for fibonacci(n)**

We have to consider that the first and second elements of a Fibonacci series are 0 and 1 respectively. And any element after these two elements is the result of adding the previous two numbers.

Now the algorithm is

- If n is less than zero, print message “Invalid n”.
- If n is 1, return 0.
- If n is 2, return 1.
- If n is greater than 2, return the sum of fibonacci(n-1) and fibonacci(n-2).

**Input**

`n`

, where `n > 0`

**Python Program**

```
def fibonacci(n) :
if n < 0:
print('Invalid n')
return
elif n == 1:
return 0
elif n == 2:
return 1
else:
return fibonacci(n-1) + fibonacci(n-2)
n = int(input('Enter n : '))
result = fibonacci(n)
print(f'{n}-Fibonacci Number : {result}')
```

**Output**

```
Enter n : 10
10-Fibonacci Number : 34
```

## 2. Nth Fibonacci Number using For Loop

In the following program, we write a function fibonacci() that can take n as argument, and return the nth Fibonacci number.

**Algorithm for fibonacci(n)**

We have to consider that the first and second elements of a Fibonacci series are 0 and 1 respectively. And any element after these two elements is the result of adding the previous two numbers, and we shall use For Loop in this example.

Now the algorithm is

- If n is less than zero, print message “Invalid n”.
- If n is 1, return 0.
- If n is 2, return 1.
- If n is greater than 2, use For Loop in the range of (2, n) to compute fibonacci series, and returning the lat element.

**Input**

`n`

, where `n > 0`

**Python Program**

```
def fibonacci(n) :
if n < 0:
print('Invalid n')
return
elif n == 1:
return 0
elif n == 2:
return 1
else:
a = 0 #previous element
b = 1 #previous to previous element
c = 0 #current element
for i in range(2, n):
c = a + b
a = b
b = c
return c
n = int(input('Enter n : '))
result = fibonacci(n)
print(f'{n}-Fibonacci Number : {result}')
```

**Output**

```
Enter n : 10
10-Fibonacci Number : 34
```

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