Skip to content
Related Articles
Sum of the first N terms of the series 2,10, 30, 68,….
• Last Updated : 25 Feb, 2021

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```

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

 ``

## Javascript

 ``
Output:
`Sum = 42`

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

My Personal Notes arrow_drop_up