Find the Nth term of the series 5, 13, 37, 109, 325, . . .

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Given a positive integer N. The task is to find Nth term of the series 5, 13, 37, 109, 325, …..

Examples:

Input: N = 5
Output: 325
Explanation: From the sequence it can be seen that the 5th term is 325

Input: N = 1
Output: 5
Explanation: The 1st term of the given sequence is 5

Approach: The sequence formed by using the following pattern. For any value N

T_N = 4 * 3^{N – 1} + N

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 calcNum(int N) 
{ 
  return 4 * pow(3, N - 1) + 1; 
}

// Driver Code
int main()
{
    int N = 5;

    cout << calcNum(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 calcNum(int N) 
  { 
    return 4 * (int)Math.pow(3, N - 1) + 1; 
  }

  // Driver Code
  public static void main(String args[])
  {
    int N = 5;
    System.out.println(calcNum(N));
  }
}

// This code is contributed by Samim Hossain Mondal.

Python3

# Python 3 program for the above approach

# Function to return Nth term
# of the series
def calcNum(N):
    
    return 4 * pow(3, N - 1) + 1

# Driver Code
if __name__ == "__main__":

    N=5

    print(calcNum(N))

# This code is contributed by Abhishek Thakur.

C#

// C# program to implement
// the above approach
using System;

public class GFG{

  // Function to return Nth term
  // of the series
  static int calcNum(int N) 
  { 
    return 4 * (int)Math.Pow(3, N - 1) + 1; 
  }

  // Driver Code
  static public void Main ()
  {
    int N = 5;
    Console.Write(calcNum(N));
  }
}


// This code is contributed by SHubham Singh

Javascript

 <script>
        // JavaScript code for the above approach

        // Function to return Nth term
        // of the series
        function calcNum(N) {
            return 4 * Math.pow(3, N - 1) + 1;
        }

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

  // This code is contributed by Potta Lokesh
    </script>

Output

Time Complexity: O(log₂N), where N represents the given integer.
Auxiliary Space: O(1), no extra space is required.

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Last Updated :
21 Sep, 2022