Find the Nth term of the series 2, 15, 41, 80, 132…

Given a number N, the task is to find the Nth term of the series 2, 15, 41, 80, 132….

Examples:

Input: N = 2
Output: 15

Input: N = 5
Output: 132

Approach: From the given series, the formula for Nth term can be found as:



1st term = 2
2nd term = 2 + 1 * 13 = 15
3rd term = 15 + 2 * 13 = 41
4th term = 41 + 3 * 13 = 80
.
.
Nth term = (N - 1)th term
         + (N - 1) * 13

Therefore, the Nth term of the series is given as
(N - 1)^{th} \text{ term} + (N - 1) * 13

Below are the steps to find the Nth term using recursion:

Recursively iterate from value N:

  • Base case: If the value called recursively is 1, then it is the first term of the series. Therefore return 2 from the function. 
    if(N == 1) 
  return 2;
  • Recursive call: If the base case is not met, then recursively iterate from the function according to the Nth term of the series: 
    (N - 1) * 13 + func(N - 1);
  • Return statement: At each recursive call(except the base case), return the recursive function for next iteration. 
    return ((13 * (N - 1))
       + func(N, i + 1));

Below is the implementation of the above approach:

C++

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// C++ program for the above approach
  
#include <bits/stdc++.h>
using namespace std;
  
// Recursive function to find Nth term
int nthTerm(int N)
{
    // Base Case
    if (N == 1) {
        return 2;
    }
  
    // Recursive Call according to
    // Nth term of the series
    return ((N - 1) * 13)
           + nthTerm(N - 1);
}
  
// Driver Code
int main()
{
    // Input Nth term
    int N = 17;
  
    // Function call
    cout << nthTerm(N) << endl;
    return 0;
}

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Java














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// Java program for the above approach 


  


class GFG{ 


  


// Recursive function to find Nth term 


static int nthTerm(int N) 


{ 


    // Base Case 


    if (N == 1)  


    { 


        return 2; 


    } 


  


    // Recursive Call according to 


    // Nth term of the series 


    return ((N - 1) * 13) + 


            nthTerm(N - 1); 


} 


  


// Driver Code 


public static void main(String[] args) 


{ 


    // Input Nth term 


    int N = 17; 


  


    // Function call 


    System.out.print(nthTerm(N) + "\n"); 


} 


} 


  


// This code is contributed by 29AjayKumar 



















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Python 3














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# Python 3 program for the above approach 


  


# Recursive function to find Nth term 


def nthTerm(N): 


      


    # Base Case 


    if (N == 1): 


        return 2


  


    # Recursive Call according to 


    # Nth term of the series 


    return ((N - 1) * 13) + nthTerm(N - 1) 


  


# Driver Code 


if __name__ == '__main__': 


      


    # Input Nth term 


    N = 17


  


    # Function call 


    print(nthTerm(N)) 


  


# This code is contributed by Bhupendra_Singh 



















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C#














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// C# program for the above approach 


using System; 


  


public class GFG{ 


  


// Recursive function to find Nth term 


static public int nthTerm(int N) 


{ 


    // Base Case 


    if (N == 1) 


    { 


        return 2; 


    } 


      


    // Recursive Call according to 


    // Nth term of the series 


    return ((N - 1) * 13) + nthTerm(N - 1); 


} 


      


// Driver Code 


static public void Main () 


{ 


    // Input Nth term 


    int N = 17; 


      


    // Function call 


    Console.WriteLine(nthTerm(N)); 


} 


} 


  


//This code is contributed by shubhamsingh10 



















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Output:


1770







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