# 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

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 <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

`// 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

`# 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#

`// 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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