# Find the sum of the series 2, 5, 13, 35, 97…

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

2, 5, 13, 35, 97, …

**Examples:**

Input: N = 2 Output: 7 The sum of first 2 terms of Series is 2 + 5 = 7 Input: N = 4 Output: 55 The sum of first 4 terms of Series is 2 + 5 + 13 + 35 = 55

**Approach: ** From this given series we find it is the sum of the Two **GP** series with common ratioes 2, 3 .

Sn = 2 + 5 + 13 + 35 + 97 … + upto nth term

Sn = (2^0 + 3^ 0) + (2^1 + 3^1) + (2^2 + 3^2) + (2^3 + 3^3)+ (2^4 + 3^4) …… + upto nth term

Sn = (2^0 + 2^1 + 2^2 + 2^3 + 2^4 … + upto nth term) + ( 3^0 + 3^1 + 3^2 + 3^3 …… + unto nth term )

Since, We know that the sum of n terms of the **GP** is given by the following formula:

Below is the implementation of the above approach:

## C++

`// C++ program for finding the sum ` `// of first N terms of the series. ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// CalculateSum function returns the final sum ` `int` `calculateSum(` `int` `n) ` `{ ` ` ` `// r1 and r2 are common ratios ` ` ` `// of 1st and 2nd series ` ` ` `int` `r1 = 2, r2 = 3; ` ` ` ` ` `// a1 and a2 are common first terms ` ` ` `// of 1st and 2nd series ` ` ` `int` `a1 = 1, a2 = 1; ` ` ` ` ` `return` `a1 * (` `pow` `(r1, n) - 1) / (r1 - 1) ` ` ` `+ a2 * (` `pow` `(r2, n) - 1) / (r2 - 1); ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `n = 4; ` ` ` ` ` `// function calling for 4 terms ` ` ` `cout << ` `"Sum = "` `<< calculateSum(n) ` ` ` `<< endl; ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`//Java program for finding the sum ` `//of first N terms of the series. ` ` ` `public` `class` `GFG { ` ` ` ` ` `//CalculateSum function returns the final sum ` ` ` `static` `int` `calculateSum(` `int` `n) ` ` ` `{ ` ` ` `// r1 and r2 are common ratios ` ` ` `// of 1st and 2nd series ` ` ` `int` `r1 = ` `2` `, r2 = ` `3` `; ` ` ` ` ` `// a1 and a2 are common first terms ` ` ` `// of 1st and 2nd series ` ` ` `int` `a1 = ` `1` `, a2 = ` `1` `; ` ` ` ` ` `return` `(` `int` `)(a1 * (Math.pow(r1, n) - ` `1` `) / (r1 - ` `1` `) ` ` ` `+ a2 * (Math.pow(r2, n) - ` `1` `) / (r2 - ` `1` `)); ` ` ` `} ` ` ` ` ` `//Driver code ` ` ` `public` `static` `void` `main(String[] args) { ` ` ` ` ` `int` `n = ` `4` `; ` ` ` ` ` `// function calling for 4 terms ` ` ` `System.out.println(` `"Sum = "` `+calculateSum(n)); ` ` ` `} ` `} ` |

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## Python 3

`# Python 3 program for finding the sum ` `# of first N terms of the series. ` ` ` `# from math import everything ` `from` `math ` `import` `*` ` ` `# CalculateSum function returns the final sum ` `def` `calculateSum(n) : ` ` ` ` ` `# r1 and r2 are common ratios ` ` ` `# of 1st and 2nd series ` ` ` `r1, r2 ` `=` `2` `, ` `3` ` ` ` ` `# a1 and a2 are common first terms ` ` ` `# of 1st and 2nd series ` ` ` `a1, a2 ` `=` `1` `, ` `1` ` ` ` ` `return` `(a1 ` `*` `(` `pow` `(r1, n) ` `-` `1` `) ` `/` `/` `(r1 ` `-` `1` `) ` ` ` `+` `a2 ` `*` `(` `pow` `(r2, n) ` `-` `1` `) ` `/` `/` `(r2 ` `-` `1` `)) ` ` ` `# Driver Code ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` ` ` `n ` `=` `4` ` ` ` ` `# function calling for 4 terms ` ` ` `print` `(` `"SUM = "` `,calculateSum(n)) ` ` ` ` ` `# This code is contributed by ANKITRAI1 ` |

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## C#

`// C# program for finding the sum ` `// of first N terms of the series. ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `// CalculateSum function ` `// returns the final sum ` `static` `int` `calculateSum(` `int` `n) ` `{ ` `// r1 and r2 are common ratios ` `// of 1st and 2nd series ` `int` `r1 = 2, r2 = 3; ` ` ` `// a1 and a2 are common first ` `// terms of 1st and 2nd series ` `int` `a1 = 1, a2 = 1; ` ` ` `return` `(` `int` `)(a1 * (Math.Pow(r1, n) - 1) / (r1 - 1) + ` ` ` `a2 * (Math.Pow(r2, n) - 1) / (r2 - 1)); ` `} ` ` ` `// Driver code ` `static` `public` `void` `Main () ` `{ ` ` ` `int` `n = 4; ` ` ` ` ` `// function calling for 4 terms ` ` ` `Console.Write(` `"Sum = "` `+ ` ` ` `calculateSum(n)); ` `} ` `} ` ` ` `// This code is contributed by Raj ` |

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## PHP

`<?php ` `// PHP program for finding the sum ` `// of first N terms of the series. ` ` ` `// CalculateSum function returns ` `// the final sum ` `function` `calculateSum(` `$n` `) ` `{ ` ` ` `// r1 and r2 are common ratios ` ` ` `// of 1st and 2nd series ` ` ` `$r1` `= 2; ` ` ` `$r2` `= 3; ` ` ` ` ` `// a1 and a2 are common first ` ` ` `// terms of 1st and 2nd series ` ` ` `$a1` `= 1; ` ` ` `$a2` `= 1; ` ` ` ` ` `return` `$a1` `* (pow(` `$r1` `, ` `$n` `) - 1) / ` ` ` `(` `$r1` `- 1) + ` `$a2` `* ` ` ` `(pow(` `$r2` `, ` `$n` `) - 1) / ` ` ` `(` `$r2` `- 1); ` `} ` ` ` `// Driver code ` `$n` `= 4; ` ` ` `// function calling for 4 terms ` `echo` `"Sum = "` `, calculateSum(` `$n` `); ` ` ` `// This code is contributed by ash264 ` `?> ` |

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**Output:**

Sum = 55

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