# Find the Nth element of the modified Fibonacci series

• Difficulty Level : Basic
• Last Updated : 13 Sep, 2022

Given two integers A and B which are the first two terms of the series and another integer N. The task is to find the Nth number using Fibonacci rule i.e. fib(i) = fib(i – 1) + fib(i – 2)
Example:

Input: A = 2, B = 3, N = 4
Output:
The series will be 2, 3, 5, 8, 13, 21, …
And the 4th element is 8.
Input: A = 5, B = 7, N = 10
Output: 343

Approach: Initialize variable sum = 0 that stores sum of the previous two values. Now, run a loop from i = 2 to N and for each index update value of sum = A + B and A = B, B = sum. Then finally, return the sum which is the required Nth element.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to return the Nth number of``// the modified Fibonacci series where``// A and B are the first two terms``int` `findNthNumber(``int` `A, ``int` `B, ``int` `N)``{` `    ``// To store the current element which``    ``// is the sum of previous two``    ``// elements of the series``    ``int` `sum = 0;` `    ``// This loop will terminate when``    ``// the Nth element is found``    ``for` `(``int` `i = 2; i < N; i++) {``        ``sum = A + B;` `        ``A = B;` `        ``B = sum;``    ``}` `    ``// Return the Nth element``    ``return` `sum;``}` `// Driver code``int` `main()``{``    ``int` `A = 5, B = 7, N = 10;` `    ``cout << findNthNumber(A, B, N);` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``import` `java.util.*;` `class` `GFG``{` `    ``// Function to return the Nth number of``    ``// the modified Fibonacci series where``    ``// A and B are the first two terms``    ``static` `int` `findNthNumber(``int` `A, ``int` `B, ``int` `N)``    ``{` `        ``// To store the current element which``        ``// is the sum of previous two``        ``// elements of the series``        ``int` `sum = ``0``;` `        ``// This loop will terminate when``        ``// the Nth element is found``        ``for` `(``int` `i = ``2``; i < N; i++)``        ``{``            ``sum = A + B;` `            ``A = B;` `            ``B = sum;``        ``}` `        ``// Return the Nth element``        ``return` `sum;``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `A = ``5``, B = ``7``, N = ``10``;` `        ``System.out.println(findNthNumber(A, B, N));``    ``}``}` `// This code is contributed by PrinciRaj1992`

## Python3

 `# Python3 implementation of the approach` `# Function to return the Nth number of``# the modified Fibonacci series where``# A and B are the first two terms``def` `findNthNumber(A, B, N):` `    ``# To store the current element which``    ``# is the sum of previous two``    ``# elements of the series``    ``sum` `=` `0` `    ``# This loop will terminate when``    ``# the Nth element is found``    ``for` `i ``in` `range``(``2``, N):``        ``sum` `=` `A ``+` `B` `        ``A ``=` `B` `        ``B ``=` `sum``    ` `    ``# Return the Nth element``    ``return` `sum` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``A ``=` `5``    ``B ``=` `7``    ``N ``=` `10` `    ``print``(findNthNumber(A, B, N))` `# This code is contributed by Ashutosh450`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG``{` `    ``// Function to return the Nth number of``    ``// the modified Fibonacci series where``    ``// A and B are the first two terms``    ``static` `int` `findNthNumber(``int` `A, ``int` `B, ``int` `N)``    ``{` `        ``// To store the current element which``        ``// is the sum of previous two``        ``// elements of the series``        ``int` `sum = 0;` `        ``// This loop will terminate when``        ``// the Nth element is found``        ``for` `(``int` `i = 2; i < N; i++)``        ``{``            ``sum = A + B;` `            ``A = B;` `            ``B = sum;``        ``}` `        ``// Return the Nth element``        ``return` `sum;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``int` `A = 5, B = 7, N = 10;` `        ``Console.WriteLine(findNthNumber(A, B, N));``    ``}``}` `// This code is contributed by AnkitRai01`

## Javascript

 ``

Output:

`343`

Time Complexity: O(N)

Auxiliary Space: O(1)

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