# Nth term of a Custom Fibonacci series

Given three integers A, B and N. A Custom Fibonacci series is defined as F(x) = F(x – 1) + F(x + 1) where F(1) = A and F(2) = B. Now the task is to find the Nth term of this series.

Examples:

Input: A = 10, B = 17, N = 3
Output: 7
10, 17, 7, -10, -17, …

Input: A = 50, B = 12, N = 10
Output: -50

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

Approach: It can be observed that the series will go on like A, B, B – A, -A, -B, A – B, A, B, B – A, …

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the Custom Fibonacci series ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to return the nth term ` `// of the required sequence ` `int` `nth_term(``int` `a, ``int` `b, ``int` `n) ` `{ ` `    ``int` `z = 0; ` `    ``if` `(n % 6 == 1) ` `        ``z = a; ` `    ``else` `if` `(n % 6 == 2) ` `        ``z = b; ` `    ``else` `if` `(n % 6 == 3) ` `        ``z = b - a; ` `    ``else` `if` `(n % 6 == 4) ` `        ``z = -a; ` `    ``else` `if` `(n % 6 == 5) ` `        ``z = -b; ` `    ``if` `(n % 6 == 0) ` `        ``z = -(b - a); ` `    ``return` `z; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `a = 10, b = 17, n = 3; ` ` `  `    ``cout << nth_term(a, b, n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the ` `// Custom Fibonacci series ` `class` `GFG ` `{ ` ` `  `// Function to return the nth term ` `// of the required sequence ` `static` `int` `nth_term(``int` `a, ``int` `b, ``int` `n) ` `{ ` `    ``int` `z = ``0``; ` `    ``if` `(n % ``6` `== ``1``) ` `        ``z = a; ` `    ``else` `if` `(n % ``6` `== ``2``) ` `        ``z = b; ` `    ``else` `if` `(n % ``6` `== ``3``) ` `        ``z = b - a; ` `    ``else` `if` `(n % ``6` `== ``4``) ` `        ``z = -a; ` `    ``else` `if` `(n % ``6` `== ``5``) ` `        ``z = -b; ` `    ``if` `(n % ``6` `== ``0``) ` `        ``z = -(b - a); ` `    ``return` `z; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `a = ``10``, b = ``17``, n = ``3``; ` ` `  `    ``System.out.println(nth_term(a, b, n)); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

## Python 3

 `# Python 3 implementation of the ` `# Custom Fibonacci series ` ` `  `# Function to return the nth term ` `# of the required sequence ` `def` `nth_term(a, b, n): ` `    ``z ``=` `0` `    ``if` `(n ``%` `6` `=``=` `1``): ` `        ``z ``=` `a ` `    ``elif` `(n ``%` `6` `=``=` `2``): ` `        ``z ``=` `b ` `    ``elif` `(n ``%` `6` `=``=` `3``): ` `        ``z ``=` `b ``-` `a ` `    ``elif` `(n ``%` `6` `=``=` `4``): ` `        ``z ``=` `-``a ` `    ``elif` `(n ``%` `6` `=``=` `5``): ` `        ``z ``=` `-``b ` `    ``if` `(n ``%` `6` `=``=` `0``): ` `        ``z ``=` `-``(b ``-` `a) ` `    ``return` `z ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``a ``=` `10` `    ``b ``=` `17` `    ``n ``=` `3` ` `  `    ``print``(nth_term(a, b, n)) ` `     `  `# This code is contributed by Surendra_Gangwar `

## C#

 `// C# implementation of the ` `// Custom Fibonacci series ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `// Function to return the nth term ` `// of the required sequence ` `static` `int` `nth_term(``int` `a, ``int` `b, ``int` `n) ` `{ ` `    ``int` `z = 0; ` `    ``if` `(n % 6 == 1) ` `        ``z = a; ` `    ``else` `if` `(n % 6 == 2) ` `        ``z = b; ` `    ``else` `if` `(n % 6 == 3) ` `        ``z = b - a; ` `    ``else` `if` `(n % 6 == 4) ` `        ``z = -a; ` `    ``else` `if` `(n % 6 == 5) ` `        ``z = -b; ` `    ``if` `(n % 6 == 0) ` `        ``z = -(b - a); ` `    ``return` `z; ` `} ` ` `  `// Driver code ` `static` `public` `void` `Main () ` `{ ` `    ``int` `a = 10, b = 17, n = 3; ` ` `  `    ``Console.Write(nth_term(a, b, n)); ` `} ` `} ` ` `  `// This code is contributed by ajit. `

Output:

```7
```

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