# 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

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

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 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;``}`

## 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 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));``  ` `}``}`

## Python3

 `# 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`

## C#

 `// 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`

## PHP

 ``

## Javascript

 ``
Output:
`Sum = 20`

My Personal Notes arrow_drop_up