Find the Nth term in series 12, 35, 81, 173, 357, …

Given a number N, the task is to find the Nth term in series 12, 35, 81, 173, 357, …

Example:

Input: N = 2
Output: 35
2nd term = (12*2) + 11
         = 35

Input: N = 5
Output: 357
5th term = (12*(2^4))+11*((2^4)-1)
         = 357

Approach:



  • Each and every number is obtained by multiplying the previous number by 2 and the addition of 11 to it.
  • Since starting number is 12.
    1st term = 12
    2nd term = (12 * 2) / 11 = 35
    3rd term = (35 * 2) / 11 = 81
    4th term = (81 * 2) / 11 = 173
    And, so on....
    
  • In general, Nth number is obtained by formula:

Below is the implementation of the above approach:

C++

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// C++ program to find the Nth term
// in series 12, 35, 81, 173, 357, ...
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to find Nth term
int nthTerm(int N)
{
    int nth = 0, first_term = 12;
  
    // Nth term
    nth = (first_term * (pow(2, N - 1)))
          + 11 * ((pow(2, N - 1)) - 1);
  
    return nth;
}
  
// Driver Method
int main()
{
    int N = 5;
    cout << nthTerm(N) << endl;
  
    return 0;
}

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Java

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// Java program to find the Nth term
// in series 12, 35, 81, 173, 357, ...
class GFG
{
  
// Function to find Nth term
static int nthTerm(int N)
{
    int nth = 0, first_term = 12;
  
    // Nth term
    nth = (int) ((first_term * (Math.pow(2, N - 1)))
        + 11 * ((Math.pow(2, N - 1)) - 1));
  
    return nth;
}
  
// Driver code
public static void main(String[] args)
{
    int N = 5;
    System.out.print(nthTerm(N) +"\n");
}
}
  
// This code is contributed by Rajput-Ji

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Python3

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# Python3 program to find the Nth term 
# in series 12, 35, 81, 173, 357, ... 
  
# Function to find Nth term 
def nthTerm(N) :
  
    nth = 0; first_term = 12
  
    # Nth term 
    nth = (first_term * (pow(2, N - 1))) + \
            11 * ((pow(2, N - 1)) - 1); 
  
    return nth; 
  
# Driver Method 
if __name__ == "__main__"
  
    N = 5
    print(nthTerm(N)) ; 
  
# This code is contributed by AnkitRai01

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C#

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// C# program to find the Nth term
// in series 12, 35, 81, 173, 357, ...
using System;
  
class GFG
{
  
// Function to find Nth term
static int nthTerm(int N)
{
    int nth = 0, first_term = 12;
  
    // Nth term
    nth = (int) ((first_term * (Math.Pow(2, N - 1)))
        + 11 * ((Math.Pow(2, N - 1)) - 1));
  
    return nth;
}
  
// Driver code
public static void Main(String[] args)
{
    int N = 5;
    Console.Write(nthTerm(N) +"\n");
}
}
  
// This code is contributed by PrinciRaj1992

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Output:

357


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