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

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  • Last Updated : 28 Jul, 2022
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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++




// 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;
}

Java




// 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

Python3




# 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

C#




// 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

Javascript




<script>
    // Javascript program to find the Nth term
    // in series 12, 35, 81, 173, 357, ...
     
    // Function to find Nth term
    function nthTerm(N)
    {
        let nth = 0, first_term = 12;
 
        // Nth term
        nth = (first_term * (Math.pow(2, N - 1)))
              + 11 * ((Math.pow(2, N - 1)) - 1);
 
        return nth;
    }
   
      let N = 5;
    document.write(nthTerm(N));
 
// This code is contributed by divyeshrabadiya07.
</script>

Output: 

357

 

Time complexity: O(log N) for given input N because using inbuilt pow function

Auxiliary Space: O(1)


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