Find the Nth term of the series 1, 3, 7, 15, 31 . . .

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

1, 3, 7, 15, 31, …..

Examples:

Input: N = 5
Output: 31

Input: N = 1
Output: 1

Approach:

The sequence is formed by using the following pattern. For any value N-

T_N = 2^N – 1

Illustration:

Input: N = 5
Output: 31
Explanation:
T_N = 2^N – 1
     = 2⁵ – 1
     = 32 – 1 
     = 31

Below is the implementation of the above approach:

C++

// C++ program to implement
// the above approach
#include <bits/stdc++.h>
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 = 5;
    cout << findTerm(N);
    return 0;
}

Java

// Java program to implement
// the above approach
import java.util.*;

public 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 = 5;
    System.out.println(findTerm(N));

  }
}

// This code is contributed by Samim Hossain Mondal.

Python

# Python program to implement
# the above approach

# Function to return
# Nth term of the series
def findTerm(N):

    return pow(2, N) - 1

# Driver Code
N = 5
print(findTerm(N))

# This code is contributed by samim2000.

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 = 5;
    Console.Write(findTerm(N));

  }
}

// This code is contributed by Samim Hossain Mondal.

Javascript

<script>
// Javascript program to implement
// the above approach

// Function to return
// Nth term of the series
function findTerm(N)
{
    return Math.pow(2, N) - 1;
}

// Driver Code
let N = 5;
document.write(findTerm(N));

// This code is contributed by saurabh_jaiswal.
</script>

Output

31

Time Complexity: O(logN) since using inbuilt pow function

Auxiliary Space: O(1)