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: 163Input: 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 <bits/stdc++.h>using namespace std;// Function to return Nth term// of the seriesint calcNum(int N){ return 2 * pow(3, N - 1) + 1;}// Driver Codeint main(){ int N = 5; cout << calcNum(N); return 0;} |
Java
// Java code to implement the above approachimport 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 seriesdef calcNum(N): return 2 * (3 ** (N - 1)) + 1# Driver CodeN = 5print(calcNum(N))# This code is contributed by gfgking |
C#
// C# code to implement the above approachusing 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)
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