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

• Last Updated : 31 May, 2022

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

Sn = 5 + 12 + 23 + 38 + â€¦ upto n terms

Examples:

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

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

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

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## Javascript

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Output:

`Sum = 40`

Time Complexity: O(1), the code will run in a constant time.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

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