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

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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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

 ` `

Output:

```Sum = 34
```

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