Nth term of a Custom Fibonacci series

• Last Updated : 31 Mar, 2021

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:
10, 17, 7, -10, -17, …
Input: A = 50, B = 12, N = 10
Output: -50

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 sequenceint 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 codeint main(){    int a = 10, b = 17, n = 3;     cout << nth_term(a, b, n);     return 0;}

Java

 // Java implementation of the// Custom Fibonacci seriesclass GFG{ // Function to return the nth term// of the required sequencestatic 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 codepublic 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 sequencedef 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 codeif __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 seriesusing System; class GFG{     // Function to return the nth term// of the required sequencestatic 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 codestatic public void Main (){    int a = 10, b = 17, n = 3;     Console.Write(nth_term(a, b, n));}} // This code is contributed by ajit.

Javascript


Output:
7

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