# Find the Nth term of the series 3, 5, 9, 17, 33. . .

Last Updated : 16 Aug, 2022

Given a positive integer N, the task is to find Nth term of the series-

3, 5, 9, 17, 33…till N terms

Examples:

Input: N = 4
Output: 17

Input: N = 3
Output: 9

Approach:

Consider the below example:

Lets say N = 4

The 4th term of the given series is 17, i.e. : 2 ^ 4 + 1 = 16 + 1 = 17

Similarly, lets say N = 3

The 3rd term of the given series is : 2 ^ 3 + 1 = 8 + 1 = 9 (which is correct).

Therefore, we can find out the relation for Nth term of the series using above observations:

1st term = 3 = 21 + 1

2nd term = 22 + 1 = 5

3rd term = 23 + 1 = 9

4th term = 24 + 1 = 17

.

.

Therefore, Nth term can be found out using following relation: 2N + 1

Upon generalising, the relation for Nth term can be represented as:

Below is the implementation of the above approach-

## C++

 `// C++ program to implement``// the above approach``#include ``using` `namespace` `std;` `// Function to return Nth``// term of the series``int` `findTerm(``int` `N)``{``    ``return` `pow``(2, N) + 1;``}` `// Driver Code``int` `main()``{``    ``int` `N = 6;``    ``cout << findTerm(N);``    ``return` `0;``}`

## Java

 `// Java program to implement``// the above approach``import` `java.io.*;` `class` `GFG {` `  ``// Function to return Nth``  ``// term of the series``  ``static` `int` `findTerm(``int` `N)``  ``{``    ``return` `(``int``)Math.pow(``2``, N) + ``1``;``  ``}` `  ``// Driver Code``  ``public` `static` `void` `main (String[] args)``  ``{``    ``int` `N = ``6``;``    ``System.out.print(findTerm(N));``  ``}``}` `// This code is contributed by Shubham Singh`

## Python3

 `# Python program to implement``# the above approach` `# Function to return Nth``# term of the series``def` `findTerm(N):``    ``return` `(``2` `*``*` `N) ``+` `1``;` `# Driver Code``N ``=` `6``;``print``(findTerm(N));` `# This code is contributed by gfgking`

## C#

 `// C# program to implement``// the above approach``using` `System;``class` `GFG``{` `  ``// Function to return Nth``  ``// term of the series``  ``static` `int` `findTerm(``int` `N)``  ``{``    ``return` `(``int``)Math.Pow(2, N) + 1;``  ``}` `  ``// Driver Code``  ``public` `static` `void` `Main()``  ``{``    ``int` `N = 6;``    ``Console.Write(findTerm(N));``  ``}``}` `// This code is contributed by Samim Hossain Mondal.`

## Javascript

 ``

Output
`65`

Time Complexity: O(logN) because it using inbuilt pow function
Auxiliary Space: O(1)

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