Find the Nth element of the modified Fibonacci series

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: 8
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: Intilalize 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++

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// C++ implementation of the approach
#include <iostream>
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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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Output:

343


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