# 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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 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++

 // C++ program for the above approach     #include  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;  }

## Java

 // 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

## Python 3

 # 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

## C#

 // 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

Output:

1770


Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.