# 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

**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 <bits/stdc++.h> ` `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; ` `} ` |

*chevron_right*

*filter_none*

## 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 ` `} ` |

*chevron_right*

*filter_none*

## 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 ` |

*chevron_right*

*filter_none*

## 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; ` ` ` `} ` `} ` |

*chevron_right*

*filter_none*

## PHP

`<?php ` `// PHP program to find sum ` `// of first n terms ` ` ` `// Function to calculate the sum ` `function` `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 ` `echo` `"Sum = "` `, calculateSum(` `$n` `); ` ` ` `// This code is contributed ` `// by anuj_67 ` `?> ` |

*chevron_right*

*filter_none*

**Output:**

Sum = 42

Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: **DSA Self Paced**. Become industry ready at a student-friendly price.

## Recommended Posts:

- Find n terms of Fibonacci type series with given first two terms
- Sum of the first N terms of the series 2, 6, 12, 20, 30....
- Sum of the first N terms of the series 5,12, 23, 38....
- Sum of the series 5+55+555+.. up to n terms
- Sum of first n terms of a given series 3, 6, 11, .....
- Find the sum of n terms of the series 1,8,27,64 ....
- Print the first N terms of the series 6, 28, 66, 120, 190, 276, ...
- Sum of the series 0.6, 0.06, 0.006, 0.0006, ...to n terms
- Find the sum of first N terms of the series 2*3*5, 3*5*7, 4*7*9, ...
- Sum of the series 1 / 1 + (1 + 2) / (1 * 2) + (1 + 2 + 3) / (1 * 2 * 3) + - - - - - - upto n terms.
- Sum of the series 0.7, 0.77, 0.777, ... upto n terms
- Sum of series 2/3 - 4/5 + 6/7 - 8/9 + ------- upto n terms
- Find the sum of all the terms in the n-th row of the given series
- Find the sum of first N terms of the series 2×3 + 4×4 + 6×5 + 8×6 + ...
- Sum of the series (1*2) + (2*3) + (3*4) + ...... upto n terms
- Find Sum of Series 1^2 - 2^2 + 3^2 - 4^2 ..... upto n terms
- Find the Sum of the series 1 + 1/3 + 1/5 + 1/7 + ... till N terms
- Program to print the series 2, 1, 4, 3, 6, 5, .... up to N terms
- Find the Sum of the series 1, 2, 3, 6, 9, 18, 27, 54, ... till N terms
- Find the Sum of the series 1/2 - 2/3 + 3/4 - 4/5 + ... till N terms

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.