# Sum of first n term of Series 3, 5, 9, 17, 33….

• Difficulty Level : Easy
• Last Updated : 27 Apr, 2021

Given n, we need to find sum of first n terms of the series represented as Sn = 3 + 5 + 9 + 17 + 33 … upto n
Examples:

```Input : 2
Output : 8
3 + 5 = 8

Input : 5
Output : 67
3 + 5 + 9 + 17 + 33 = 67```

Let, the nth term be denoted by tn.
This problem can easily be solved by splitting each term as follows :

Sn = 3 + 5 + 9 + 17 + 33……
Sn = (2+1) + (4+1) + (8+1) + (16+1) +……
Sn = (2+1) + (2*2+1) + (2*2*2+1) + (2*2*2*2+1) +……+ ((2*2*2..unto n times) + 1)

We observed that the nth term can be written in terms of powers of 2 and 1.
Hence, the sum of first n terms is given as follows:

Sn = (2+1) + (4+1) + (8+1) + (16+1) +……+ upto n terms
Sn = (1 + 1 + 1 + 1 + …unto n terms) + (2 + 4 + 8 + 16 + …upto nth power of 2)
In above formula,
2 + 4 + 8 + 16…. is a G.P.
It’s sum of first n terms is given by 2*(2^n-1)/(2-1) = 2^(n+1) – 2 (using G.P. formula)
Sn = n + 2*(2^n – 1)
Sn = 2^(n+1) + n -2

## C++

 `// C++ program to find sum of first n terms` `#include ` `using` `namespace` `std;`   `int` `calculateSum(``int` `n)` `{` `    ``// Sn = n*(4*n*n + 6*n - 1)/3` `    ``return` `(``pow``(2, n + 1) + n - 2);` `}`   `// Driver code` `int` `main()` `{` `    ``// number of terms to be included in sum` `    ``int` `n = 4;`   `    ``// find the Sn` `    ``cout << ``"Sum = "` `<< calculateSum(n);`   `    ``return` `0;` `}`

## Java

 `// Java program to find` `// sum of first n terms` `import` `java.util.*;`   `class` `GFG ` `{` `static` `int` `calculateSum(``int` `n)` `{` `    ``// Sn = n*(4*n*n + 6*n - 1)/3` `    ``return` `((``int``)Math.pow(``2``, n + ``1``) + ` `                             ``n - ``2``);` `}`   `// Driver Code` `public` `static` `void` `main(String args[])` `{` `    ``// number of terms to ` `    ``// be included in sum` `    ``int` `n = ``4``;`   `    ``// find the Sn` `    ``System.out.println(``"Sum = "` `+ ` `                ``calculateSum(n));` `}` `}`   `// This code is contributed ` `// by Kirti_Mangal`

## Python

 `# Python program to find sum ` `# of n terms of the series` `def` `calculateSum(n):`   `    ``return` `(``2``*``*``(n ``+` `1``) ``+` `n ``-` `2``)`   `# Driver Code`   `# number of terms for the sum` `n ``=` `4`   `# find the Sn` `print``(``"Sum ="``, calculateSum(n))`   `# This code is contributed ` `# by Surendra_Gangwar`

## C#

 `//C# program to find` `// sum of first n terms` `using` `System;`   `class` `GFG ` `{` `static` `int` `calculateSum(``int` `n)` `{` `    ``// Sn = n*(4*n*n + 6*n - 1)/3` `    ``return` `((``int``)Math.Pow(2, n + 1) + ` `                            ``n - 2);` `}`   `// Driver Code` `public` `static` `void` `Main()` `{` `    ``// number of terms to ` `    ``// be included in sum` `    ``int` `n = 4;`   `    ``// find the Sn` `    ``Console.WriteLine(``"Sum = "` `+ ` `                ``calculateSum(n));` `}` `}`   `// This code is contributed ` `// by inder_verma..`

## PHP

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## Javascript

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Output:

`Sum = 34`

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