Our Objective

To implement a recursive function that generates the Fibonacci sequence up to a certain number of terms.

The Theory

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1.

The function takes an argument 'n', which represents the number of terms in the sequence to be generated. If 'n' is less than or equal to 1, the function returns 'n'. Otherwise, the function calls itself recursively twice with 'n-1' and 'n-2' as arguments and adds the results together to get the n'th term in the sequence.

In this modified version of the program, instead of starting the sequence with 0 and 1, it starts with 'a' and 'b'. If 'n' is less than or equal to 1, the function returns 'a' or 'b' depending on whether 'n' is 0 or 1, respectively. Otherwise, the function returns the concatenation of the previous two terms in the sequence, represented by recur_fibo(n-1) and recur_fibo(n-2).

The program then takes an input nterms, which represents the number of terms in the sequence to be generated, and checks if it is greater than 0. If 'nterms' is less than or equal to 0, the program prints an error message. Otherwise, it prints a message indicating that it is generating the Fibonacci sequence, and uses a loop to call the recur_fibo function with each value of 'i' in the range from 0 to 'nterms-1' and prints the result.

Overall, this program uses recursion to generate the Fibonacci sequence up to a given number of terms and allows for a different starting point in the sequence.

Learning Outcomes

• Understanding of recursion: The program uses a recursive function to generate the Fibonacci sequence. By studying this program, one can gain a better understanding of how recursion works and how to apply it to solve problems.
• Understanding of conditional statements: The program also makes use of conditional statements to check if the input is valid and to determine the value of the Fibonacci sequence. By studying this program, one can learn how to write effective conditional statements.
• Understanding of loops: The program uses a for loop to generate the Fibonacci sequence. By studying this program, one can learn how to use loops to perform repetitive tasks.
• Understanding of modular programming: The program uses a modular approach to solve the problem, breaking it down into smaller, more manageable parts. By studying this program, one can learn how to write modular code that is easier to read, maintain, and debug.