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

  • Last Updated : 28 Jan, 2022

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 

TN = 4 * 3N – 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
325

Time Complexity: O(1)
Auxiliary Space: O(1)


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