# 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 = 2Output:15Input:N = 5Output: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;` `}` |

## 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` |

## Javascript

`<script>` `// javascript program for the above approach` `// Recursive function to find Nth term` `function` `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` ` ` `// Input Nth term` ` ` `let N = 17;` ` ` `// Function call` ` ` `document.write( nthTerm(N) );` ` ` `// This code is contributed by Rajput-Ji` `</script>` |

**Output:**

1770

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