# Find sum of N-th group of Natural Numbers

Given a series of natural numbers divided into groups as: (1, 2), (3, 4, 5, 6), (7, 8, 9, 10, 11, 12), (13, 14, 15, 16, 17, 18, 19, 20)….. and so on. Given a number N, the task is to find the sum of the numbers in the N^{th} group.

**Examples:**

Input: N = 3Output: 57 Numbers in 3rd group are: 7, 8, 9, 10, 11, 12Input: N = 10Output: 2010

The first group has **2** terms,

the second group has **4** terms,

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.

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the nth group has **2n** terms.

Now,

The last term of the **first group** is 2 = 1 × (1 + 1)

The last term of the **second group** is 6 = 2 × (2 + 1)

The last term of the **third group** is 12 = 3 × (3 + 1)

The last term of the **fourth group** is 20 = 4 × (4 + 1)

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.

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The last term of the **nth group = n(n + 1)**.

Therefore, the sum of the numbers in the **nth group** is:

= sum of all the numbers upto

nth group– sum of all the numbers upto(n – 1)th group

= [1 + 2 +……..+ n(n + 1)] – [1 + 2 +……..+ (n – 1 )((n – 1) + 1)]

=

=

=

=

Below is the implementation of the above approach:

## C++

`// C++ program to find sum in Nth group` `#include<bits/stdc++.h>` `using` `namespace` `std;` `//calculate sum of Nth group` `int` `nth_group(` `int` `n){` ` ` `return` `n * (2 * ` `pow` `(n, 2) + 1);` `}` `//Driver code` `int` `main()` `{` ` ` `int` `N = 5;` ` ` `cout<<nth_group(N);` ` ` ` ` `return` `0;` `}` |

## Java

`// Java program to find sum` `// in Nth group` `import` `java.util.*;` `class` `GFG` `{` `// calculate sum of Nth group` `static` `int` `nth_group(` `int` `n)` `{` ` ` `return` `n * (` `2` `* (` `int` `)Math.pow(n, ` `2` `) + ` `1` `);` `}` `// Driver code` `public` `static` `void` `main(String arr[])` `{` ` ` `int` `N = ` `5` `;` ` ` `System.out.println(nth_group(N));` `}` `}` `// This code is contributed by Surendra` |

## Python3

`# Python program to find sum in Nth group` `# calculate sum of Nth group` `def` `nth_group(n):` ` ` `return` `n ` `*` `(` `2` `*` `pow` `(n, ` `2` `) ` `+` `1` `)` `# Driver code` `N ` `=` `5` `print` `(nth_group(N))` |

## C#

`// C# program to find sum in Nth group` `using` `System;` `class` `gfg` `{` ` ` `//calculate sum of Nth group` ` ` `public` `static` `double` `nth_group(` `int` `n)` ` ` `{` ` ` `return` `n * (2 * Math.Pow(n, 2) + 1);` ` ` `}` ` ` `//Driver code` ` ` `public` `static` `int` `Main()` ` ` `{` ` ` `int` `N = 5;` ` ` `Console.WriteLine(nth_group(N));` ` ` `return` `0;` ` ` `}` `}` `// This code is contributed by Soumik` |

## PHP

`<?php` `// PHP program to find sum` `// in Nth group` `// calculate sum of Nth group` `function` `nth_group(` `$n` `)` `{` ` ` `return` `$n` `* (2 * pow(` `$n` `, 2) + 1);` `}` `// Driver code` `$N` `= 5;` `echo` `nth_group(` `$N` `);` `// This code is contributed` `// by jit_t` `?>` |

## Javascript

`<script>` ` ` `// Javascript program to find sum in Nth group` ` ` ` ` `//calculate sum of Nth group` ` ` `function` `nth_group(n)` ` ` `{` ` ` `return` `n * (2 * Math.pow(n, 2) + 1);` ` ` `}` ` ` ` ` `let N = 5;` ` ` `document.write(nth_group(N));` ` ` `</script>` |

**Output:**

255