In the previous article, we have discussed Python Program to Check if Three Points are Collinear

Given a number N the task is to find the Nth Pentagonal Number in Python.

**Nth Pentagonal Number:**

n is the nth pentagonal number. When the pentagons are overlapped so that they share one vertex, Pn is the number of different dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots.

A polygonal number (triangular number, square number, and so on) is a number that is represented as dots or pebbles ordered in the shape of a regular polygon. The first few pentagonal numbers are as follows: 1, 5, 12, and so on.

**Examples:**

**Example1:**

**Input:**

Given Number = 4

**Output:**

The { 4 } pentagonal number = 22

**Example2:**

**Input:**

Given Number = 6

**Output:**

The { 6 } pentagonal number = 51

## Program to Find N’th Pentagonal Number in Python

Below are the ways to find the Nth Pentagonal Number in Python:

Nth Pentagonal Number Formula =

3*n*(n-1)/2 + n (or) (3*n*n – n)/2

### Method #1: Using Mathematical Formula (Static Input)

**Approach:**

- Give the number N as static Input and store it in a variable.
- Create a function
**nthPentagonalNumb()**which accepts the given number as an argument and returns the nth pentagonal number. - Inside the
**nthPentagonalNumb()**function. - Calculate the value of (3*n*n – n)/2 where n is the argument and store it in a variable say
**reslt**. - Return the
**reslt.** - Pass the given Number as an argument to
**nthPentagonalNumb()**function and store the result returned from the function in a variable say**nthNumb**. - Print the
**nthNumb**value. - The Exit of the Program.

**Below is the implementation:**

# Create a function nthPentagonalNumb() which accepts the given number # as an argument and returns the nth pentagonal number. def nthPentagonalNumb(numb): # Inside the nthPentagonalNumb() function. # Calculate the value of (3*n*n - n)/2 where n is the argument and # store it in a variable say reslt. reslt = (3*numb*numb - numb)/2 # Return the reslt. return int(reslt) # Give the number N as static Input and store it in a variable. gvnnumb = 4 # Pass the given Number as an argument to nthPentagonalNumb() # function and store the result returned from the function in a variable say nthNumb. nthNumb = nthPentagonalNumb(gvnnumb) # Print the nthNumb value. print('The {', gvnnumb, '} pentagonal number = ', nthNumb)

**Output:**

The { 4 } pentagonal number = 22

### Method #2: Using Mathematical Formula (User Input)

**Approach:**

- Give the number N as user Input using the int(input()) function and store it in a variable.
- Create a function
**nthPentagonalNumb()**which accepts the given number as an argument and returns the nth pentagonal number. - Inside the
**nthPentagonalNumb()**function. - Calculate the value of (3*n*n – n)/2 where n is the argument and store it in a variable say
**reslt**. - Return the
**reslt.** - Pass the given Number as an argument to
**nthPentagonalNumb()**function and store the result returned from the function in a variable say**nthNumb**. - Print the
**nthNumb**value. - The Exit of the Program.

**Below is the implementation:**

# Create a function nthPentagonalNumb() which accepts the given number # as an argument and returns the nth pentagonal number. def nthPentagonalNumb(numb): # Inside the nthPentagonalNumb() function. # Calculate the value of (3*n*n - n)/2 where n is the argument and # store it in a variable say reslt. reslt = (3*numb*numb - numb)/2 # Return the reslt. return int(reslt) # Give the number N as user Input using the int(input()) function # and store it in a variable. gvnnumb = int(input('Enter some random Number = ')) # Pass the given Number as an argument to nthPentagonalNumb() # function and store the result returned from the function in a variable say nthNumb. nthNumb = nthPentagonalNumb(gvnnumb) # Print the nthNumb value. print('The {', gvnnumb, '} pentagonal number = ', nthNumb)

**Output:**

Enter some random Number = 6 The { 6 } pentagonal number = 51

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