Sum of the first N terms of the series 2, 6, 12, 20, 30….

Given a number N, the task is to find the sum of first N terms of the below series:

Sn = 2 + 6 + 12 + 20 + 30 … upto n terms

Examples:



Input: N = 2
Output: 8
2 + 6
= 8

Input: N = 4 
Output: 40
2 + 6+ 12 + 20
= 40

Approach: Let, the nth term be denoted by tn.
This problem can easily be solved by spliting each term as follows :

Sn = 2 + 6 + 12 + 20 + 30......
Sn = (1+1^2) + (2+2^2) + (3+3^2) + (4+4^2) +......
Sn = (1 + 2 + 3 + 4 + ...unto n terms) + (1^2 + 2^2 + 3^2 + 4^2 + ...upto n terms)

We observed that Sn can broken down into summation of two series.
Hence, the sum of first n terms is given as follows:

Sn = (1 + 2 + 3 + 4 + ...unto n terms) + (1^2 + 2^2 + 3^2 + 4^2 + ...upto n terms)
Sn = n*(n + 1)/2 + n*(n + 1)*(2*n + 1)/6

Below is the implementation of above approach:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ program to find sum of first n terms
#include <bits/stdc++.h>
using namespace std;
  
// Function to calculate the sum
int calculateSum(int n)
{
  
    return n * (n + 1) / 2 + n * 
            (n + 1) * (2 * n + 1) / 6;
}
  
// Driver code
int main()
{
    // number of terms to be
    // included in the sum
    int n = 3;
  
    // find the Sn
    cout << "Sum = " << calculateSum(n);
  
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to find sum of first n terms 
  
import java.util.*;
import java.lang.*;
import java.io.*;
class GFG
{
      
// Function to calculate the sum 
static int calculateSum(int n) 
    
    return n * (n + 1) / 2 + n *  
            (n + 1) * (2 * n + 1) / 6
    
// Driver code 
public static void main(String args[]) 
    // number of terms to be 
    // included in the sum 
    int n = 3
    
    // find the Sn 
    System.out.print("Sum = " + calculateSum(n)); 
    
}

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python program to find sum of
# first n terms
  
# Function to calculate the sum
def calculateSum(n):
    return (n * (n + 1) // 2 + n * 
           (n + 1) * (2 * n + 1) // 6)
  
# Driver code
  
# number of terms to be
# included in the sum
n = 3
  
# find the Sum
print("Sum = ", calculateSum(n))
  
# This code is contributed by
# Sanjit_Prasad

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to find sum of 
// first n terms 
using System;
  
class GFG
{
      
// Function to calculate the sum 
static int calculateSum(int n) 
  
    return n * (n + 1) / 2 + n * 
               (n + 1) * (2 * n + 1) / 6; 
  
// Driver code 
public static void Main() 
    // number of terms to be 
    // included in the sum 
    int n = 3; 
  
    // find the Sn 
    Console.WriteLine("Sum = "
                       calculateSum(n)); 
}
  
// This code is contributed by inder_verma

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// PHP program to find sum
// of first n terms
  
// Function to calculate the sum
function calculateSum($n)
{
    return $n * ($n + 1) / 2 + $n
                ($n + 1) * (2 * $n + 1) / 6;
}
  
// Driver code
  
// number of terms to be
// included in the sum
$n = 3;
  
// find the Sn
echo "Sum = " , calculateSum($n);
  
// This code is contributed 
// by inder_verma
?>

chevron_right


Output:

Sum = 20


My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.