# Find sum of N-th group of Natural Numbers

• Last Updated : 10 May, 2021

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 × (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)

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#includeusing namespace std; //calculate sum of Nth groupint nth_group(int n){     return n * (2 * pow(n, 2) + 1);} //Driver codeint main(){   int N = 5;  cout<

## Java

 // Java program to find sum// in Nth groupimport java.util.*; class GFG{ // calculate sum of Nth groupstatic int nth_group(int n){    return n * (2 * (int)Math.pow(n, 2) + 1);} // Driver codepublic 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 groupdef nth_group(n):    return n * (2 * pow(n, 2) + 1) # Driver codeN = 5print(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`

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