Question

Fibonacci sequence has many applications in Computer Science. Write a program to generate Fibonacci numbers as many as desired. After the construction, you can print the sum value of the sequence. The example is below and user input is in boldface.

Answer 1

Answer:

The Python Code for Fibonacci Sequence is :

# Function for nth Fibonacci number  

def Fibonacci(n):  

if n<0:  

 print("Incorrect input")  

# First Fibonacci number is 0  

elif n==0:  

 return 0

# Second Fibonacci number is 1  

elif n==1:  

 return 1

else:  

 return Fibonacci(n-1)+Fibonacci(n-2)  

# Driver Program  

print(Fibonacci(9))  

Explanation:

The Fibonacci numbers are the numbers in the following integer sequence.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ……..

In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation

Fn = Fn-1 + Fn-2

with seed values

F0 = 0 and F1 = 1.

Answer 2

Answer:

//import the Scanner class

import java.util.Scanner;

public class FibonacciSeries {

   

   public static void main(String[] args) {

       

       //create an object of the Scanner class

       Scanner input = new Scanner(System.in);

       

       //Prompt the user to enter the number of terms

       System.out.println("Enter the number of terms");

       

       //Store the user input in a variable

       int noOfTerms = input.nextInt();

       

       //Create a variable sum to hold the sum of the series.

       int sum = 0;

       

       //Display message

       System.out.println("First " + noOfTerms + " terms of Fibonacci numbers are");

       

       //Create a loop that goes as many times as the number of terms

       //At every term (cycle), call the fibonacci method on the term.

       //And add the number to the sum variable

       for (int i = 1; i<=noOfTerms; i++){

         System.out.println(fibonacci(i));

         sum += fibonacci(i);

       }

       

       //Display a message

       System.out.println("The sum of the above sequence is ");

       

       //Display the sum of the fibonacci series

       System.out.println(sum);

   }

   

   //Create a method fibonacci to return the nth term of the fibonacci series

   public static int fibonacci(int n){

       

       //when n = 1, the fibonacci number is 0

       if (n <= 1){

           return 0;

       }

       

       //when n = 2, the fibonacci number is 1

       else if(n == 2){

           return 1;

       }

       

       //at other terms, fibonacci number is the sum of the previous two numbers

       else {

           return fibonacci(n-1) + fibonacci(n-2);

       }

       

   }     // End of fibonacci method

   

}        // End of class declaration

Sample Output:

>> Enter the number of terms

7

>> First 7 terms of Fibonacci numbers are

0

1

1

2

3

5

8

>> The sum of the above sequence is  

20

Explanation:

The above code has been written in Java. It contains comments explaining important parts of the code. Please go through the code through the comments for understandability.