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

• Last Updated : 25 Feb, 2021

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 splitting 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++

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

Java

 // Java program to find sum of first n terms import java.util.*;import java.lang.*;import java.io.*;class GFG{     // Function to calculate the sumstatic int calculateSum(int n){       return n * (n + 1) / 2 + n *             (n + 1) * (2 * n + 1) / 6;}   // Driver codepublic 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));   }}

Python3

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

C#

 // C# program to find sum of// first n termsusing System; class GFG{     // Function to calculate the sumstatic int calculateSum(int n){     return n * (n + 1) / 2 + n *               (n + 1) * (2 * n + 1) / 6;} // Driver codepublic 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



Javascript


Output:
Sum = 20

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