# Sum of the first N terms of the series 2,10, 30, 68,….

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

Sn = 2 + 10 + 30 + 68 + … upto n terms

Examples:

```Input: N = 2
Output: 12
2 + 10
= 12

Input: N = 4
Output: 40
2 + 10 + 30 + 68
= 110
```

## 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 + 10 + 30 + 68 + ......
Sn = (1+1^3) + (2+2^3) + (3+3^3) + (4+4^3) +......
Sn = (1 + 2 + 3 + 4 + ...unto n terms) + (1^3 + 2^3 + 3^3 + 4^3 + ...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) + (1^3 + 2^3 + 3^3 + 4^3 + ...upto n terms)
Sn = n*(n + 1)/2 + (n*(n + 1)/2)^2
```

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  ` `           ``+ ``pow``((n * (n + 1) / 2), 2); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``// number of terms to be ` `    ``// included in the sum ` `    ``int` `n = 3; ` ` `  `    ``// find the Sum ` `    ``cout << ``"Sum = "` `<< calculateSum(n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find sum of first n terms  ` ` `  `public` `class` `GFG { ` `     `  `    ``// Function to calculate the sum  ` `    ``static` `int` `calculateSum(``int` `n)  ` `    ``{  ` `       `  `        ``return` `n * (n + ``1``) / ``2`   `               ``+ (``int``)Math.pow((n * (n + ``1``) / ``2``), ``2``);  ` `    ``}  ` `     `  `    ``// Driver code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``// number of terms to be  ` `        ``// included in the sum  ` `        ``int` `n = ``3``;  ` `       `  `        ``// find the Sum  ` `        ``System.out.println(``"Sum = "``+ calculateSum(n));  ` `    ``} ` `    ``// This Code is contributed by ANKITRAI1 ` `} `

## Python3

 `# Python program to find sum  ` `# of first n terms ` ` `  `# Function to calculate the sum ` `def` `calculateSum(n): ` `    ``return` `(n ``*` `(n ``+` `1``) ``/``/` `2` `+`  `        ``pow``((n ``*` `(n ``+` `1``) ``/``/` `2``), ``2``)) ` ` `  `# 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 ` `    ``public` `void` `calculateSum(``int` `n) ` `    ``{ ` `        ``double` `r = (n * (n + 1) / 2 +  ` `                ``Math.Pow((n * (n + 1) / 2), 2)); ` `        ``Console.WriteLine(``"Sum = "` `+ r); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `int` `Main() ` `    ``{ ` `        ``gfg g = ``new` `gfg(); ` ` `  `        ``// number of terms to be ` `        ``// included in the sum ` `        ``int` `n = 3; ` `         `  `        ``// find the Sum ` `        ``g.calculateSum(n); ` `        ``Console.Read(); ` `        ``return` `0; ` `    ``} ` `} `

## PHP

 ` `

Output:

```Sum = 42
```

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