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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