# 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 + … 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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