# Sum of first n terms of a given series 3, 6, 11, …..

Given a series and a number n, the task is to find the sum of its first n terms. Below is the series:

3, 6, 11, 20, ….

**Examples:**

Input: N = 2 Output: 9 The sum of first 2 terms of Series is 3 + 6 = 9 Input: N = 3 Output: 20 The sum of first 3 terms of Series is 3 + 6 + 11 = 20

**Approach:** This problem can easily solved by observing that the nth term of the series :

Sn = 3 + 6 + 11 + 20 … + upto nth term

Sn = (1 + 2^1) + (2 + 2^2) + (3 + 2^3)+ (4 + 2^4) …… + upto nth term

Sn = (1 + 2 + 3 + 4 …. + upto nth term) + ( 2^1 + 2^2 + 2^3 …… + unto nth term )

We observe that Sn is a summation of two series: **AP and GP**

As we know the sum of first n terms of AP is given by

And also the Sum of first n terms of G.P is given by

Hence the total sum is given by sum of both AP and GP.

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)` `{` ` ` `// starting number` ` ` `int` `a1 = 1, a2 = 2;` ` ` `// Common Ratio` ` ` `int` `r = 2;` ` ` `// Common difference` ` ` `int` `d = 1;` ` ` `return` `(n) * (2 * a1 + (n - 1) * d) / 2 + a2` ` ` `* (` `pow` `(r, n) - 1) / (r - 1);` `}` `// Driver code` `int` `main()` `{` ` ` `// N th term to be find` ` ` `int` `n = 5;` ` ` `// 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)` `{` ` ` `// starting number` ` ` `int` `a1 = ` `1` `, a2 = ` `2` `;` ` ` `// Common Ratio` ` ` `int` `r = ` `2` `;` ` ` `// Common difference` ` ` `int` `d = ` `1` `;` ` ` `return` `(n) * (` `2` `* a1 + (n - ` `1` `) * d) / ` `2` `+ a2` ` ` `* (` `int` `)(Math.pow(r, n) - ` `1` `) / (r - ` `1` `);` `}` `// Driver code` ` ` `public` `static` `void` `main (String[] args) {` ` ` `// N th term to be find` ` ` `int` `n = ` `5` `;` ` ` `// find the Sn` ` ` `System.out.print( ` `"Sum = "` `+ calculateSum(n));` ` ` `}` `}` `// This code is contributed by inder_verma.` |

## Python3

`# Python3 program to find` `# sum of first n terms` `def` `calculateSum(n):` ` ` `# First term of AP` ` ` `a1 ` `=` `1` `;` ` ` ` ` `# First term of GP` ` ` `a2 ` `=` `2` `;` ` ` ` ` `# common ratio of GP` ` ` `r ` `=` `2` `;` ` ` ` ` `# common difference Of AP` ` ` `d ` `=` `1` `;` ` ` `return` `((n) ` `*` `(` `2` `*` `a1 ` `+` `(n ` `-` `1` `) ` `*` `d) ` `/` ` ` `2` `+` `a2 ` `*` `(` `pow` `(r, n) ` `-` `1` `) ` `/` ` ` `(r ` `-` `1` `));` `# Driver Code` `# no. of the terms` `# for the sum` `n ` `=` `5` `;` `# Find the Sn` `print` `(` `"Sum ="` `, ` `int` `(calculateSum(n)))` `# This code is contributed` `# by Surendra_Gangwar` |

## C#

`// C# program to find sum` `// of first n terms` `using` `System;` `class` `GFG` `{` `// Function to calculate the sum` `static` `int` `calculateSum(` `int` `n)` `{` ` ` `// starting number` ` ` `int` `a1 = 1, a2 = 2;` ` ` `// Common Ratio` ` ` `int` `r = 2;` ` ` `// Common difference` ` ` `int` `d = 1;` ` ` `return` `(n) * (2 * a1 + (n - 1) * d) / 2 + a2 *` ` ` `(` `int` `)(Math.Pow(r, n) - 1) / (r - 1);` `}` `// Driver code` `public` `static` `void` `Main ()` `{` ` ` `// N th term to be find` ` ` `int` `n = 5;` ` ` ` ` `// find the Sn` ` ` `Console.WriteLine(` `"Sum = "` `+ calculateSum(n));` `}` `}` `// This code is contributed` `// by inder_verma` |

## PHP

`<?php` `// PHP program to find sum of first n terms` `// Function to calculate the sum` `function` `calculateSum(` `$n` `)` `{` ` ` `// starting number` ` ` `$a1` `= 1;` ` ` `$a2` `= 2;` ` ` ` ` `// Common Ratio` ` ` `$r` `= 2;` ` ` ` ` `// Common difference` ` ` `$d` `= 1;` ` ` ` ` `return` `(` `$n` `) * (2 * ` `$a1` `+ (` `$n` `- 1) * ` `$d` `) / 2 +` ` ` `$a2` `* (pow(` `$r` `, ` `$n` `) - 1) / (` `$r` `- 1);` `}` `// Driver code` `// Nth term to be find` `$n` `= 5;` `// find the Sn` `echo` `"Sum = "` `, calculateSum(` `$n` `);` `// This code is contributed` `// by Shashank_Sharma` `?>` |

## Javascript

`<script>` `// Javascript program to find sum of first n terms` `// Function to calculate the sum` `function` `calculateSum(n)` `{` ` ` `// starting number` ` ` `let a1 = 1, a2 = 2;` ` ` `// Common Ratio` ` ` `let r = 2;` ` ` `// Common difference` ` ` `let d = 1;` ` ` `return` `(n) * (2 * a1 + (n - 1) * d) / 2 + a2` ` ` `* (Math.pow(r, n) - 1) / (r - 1);` `}` `// Driver code` ` ` `// N th term to be find` ` ` `let n = 5;` ` ` `// find the Sn` ` ` `document.write(` `"Sum = "` `+ calculateSum(n));` `// This code is contributed by Mayank Tyagi` `</script>` |

**Output:**

Sum = 77

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