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

• Difficulty Level : Easy
• Last Updated : 31 Aug, 2022

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`

Time Complexity: O(log n)

Auxiliary Space: O(log n)

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