# 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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

 ` `

Output:

```Sum = 20
```

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