# Sum of the first N terms of the series 5,12, 23, 38….

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

Sn = 5 + 12 + 23 + 38 + … upto n terms

Examples:

```Input: N = 2
Output: 17
5 + 12
= 17

Input: N = 4
Output: 80
5 + 12 + 23 + 38
= 78
```

## 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 with the help of a general formula for these type of series,

The series given above is a quadratic series. They are special because the difference of consecutive terms of this series will be in arithmetic progression.
There general formula is given by:

```General Formula = a*(n^2) + b*n + c
```

Now, by putting first 3 terms of series in general formula we can get values of a, b and c.

```Sn = 5 + 12 + 30 + 68 + ......
tn = 2 * (n^2) + n + 2
Sn = 2 * (n * (n+1) * (2 * n+1)/6) + n * (n+1)/2 + 2 * (n)

```

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` `2 * (n * (n + 1) * (2 * n + 1) / 6)  ` `               ``+ n * (n + 1) / 2 + 2 * (n); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``// number of terms to be included in 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.io.*; ` ` `  `class` `GFG { ` ` `  `// Function to calculate the sum ` ` ``static` `int` `calculateSum(``int` `n) ` `{ ` ` `  `    ``return` `2` `* (n * (n + ``1``) * (``2` `* n + ``1``) / ``6``)  ` `            ``+ n * (n + ``1``) / ``2` `+ ``2` `* (n); ` `} ` ` `  `// Driver code ` ` `  `    ``public` `static` `void` `main (String[] args) { ` `        ``// number of terms to be included in sum ` `    ``int` `n = ``3``; ` ` `  `    ``// find the Sn ` `    ``System.out.print( ``"Sum = "` `+ calculateSum(n)); ` `    ``} ` `} ` `// This code is contributed  ` `// by  anuj_67.. `

## Python 3

 `# Python program to find  ` `# sum of first n terms ` ` `  `# Function to calculate the sum  ` `def` `calculateSum(n) : ` ` `  `    ``return` `(``2` `*` `(n ``*` `(n ``+` `1``) ``*`  `           ``(``2` `*` `n ``+` `1``) ``/``/` `6``) ``+` `n ``*` `           ``(n ``+` `1``) ``/``/` `2` `+` `2` `*` `(n)) ` `         `  `# Driver code      ` `if` `__name__ ``=``=` `"__main__"` `: ` ` `  `    ``# number of terms to be ` `    ``# included in sum  ` `    ``n ``=` `3` ` `  `    ``# find the Sn  ` `    ``print``(``"Sum ="``,calculateSum(n))  ` ` `  `# This code is contributed by ANKITRAI1 `

## 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` `2 * (n * (n + 1) * (2 * n + 1) / 6) + ` `                ``n * (n + 1) / 2 + 2 * (n); ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main ()  ` `{ ` `    ``// number of terms to be ` `    ``// included in sum ` `    ``int` `n = 3; ` `     `  `    ``// find the Sn ` `    ``Console.WriteLine(``"Sum = "` `+ calculateSum(n)); ` `} ` `} ` ` `  `// This code is contributed  ` `// by Shashank `

## PHP

 ` `

Output:

```Sum = 40
```

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