Find the Nth term of the series 3, 7, 19, 55, 163, . . .

Given a positive integer N. The task is to find Nth term of the series 3, 7, 19, 55, 163, …..

Examples:

Input: N = 5
Output: 163

Input: N = 1
Output: 3

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

T_N = 2 * 3^{N – 1} + 1

Illustration:

Input: N = 5
Output: 163
Explanation:
T_N = 2 * 3^{N – 1} + 1
     = 2 * 3^{5 – 1} + 1
     = 2 * 81 + 1
     = 162 + 1
     = 163

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 2 * pow(3, N - 1) + 1;
}

// Driver Code
int main()
{
    int N = 5;
    cout << calcNum(N);
    return 0;
}

Java

// Java code to implement the above approach
import java.lang.*;
public class gfg
{

    /* Function to return the Nth term of the series */
    static int calcNum(int N)
    {
        return (int)(2*(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 Abhishek Thakur

Python3

# Python3 program to implement
# the above approach

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

    return 2 * (3 ** (N - 1)) + 1

# Driver Code
N = 5

print(calcNum(N))

# This code is contributed by gfgking

C#

// C# code to implement the above approach
using System;
public class gfg
{

  /* Function to return the Nth term of the series */
  static int calcNum(int N)
  {
    return (int)(2 * (Math.Pow(3, N - 1))) + 1;
  }

  // Driver Code
  public static void Main(string[] args)
  {
    int N = 5;

    Console.WriteLine(calcNum(N));
  }
}

// This code is contributed by Abhishek Thakur

Javascript

<script>
      // JavaScript code for the above approach


      // Function to return Nth term
      // of the series
      function calcNum(N) {
          return 2 * Math.pow(3, N - 1) + 1;
      }

      // Driver Code

      let N = 5;
      document.write(calcNum(N));

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

Output

163

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

Auxiliary Space: O(1)