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

• Last Updated : 16 Aug, 2022

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

TN = 2 * 3N – 1 + 1

Illustration:

Input: N = 5
Output: 163
Explanation:
TN = 2 * 3N – 1 + 1
= 2 * 35 – 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 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



Output

163

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

Auxiliary Space: O(1)

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