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# Find sum of N-th group of Natural Numbers

• Last Updated : 11 Aug, 2022

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 Nth group.

Examples:

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

Input : N = 10
Output : 2010 

The first group has 2 terms,
the second group has 4 terms,

the nth group has 2n terms.
Now,
The last term of the first group is 2 = 1 Ã— (1 + 1)
The last term of the second group is 6 = 2 Ã— (2 + 1)
The last term of the third group is 12 = 3 Ã— (3 + 1)
The last term of the fourth group is 20 = 4 Ã— (4 + 1)

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 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<

## 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

 

## Javascript

 

Output:

255`

Time Complexity: O(1)

Auxiliary Space: O(1)

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