On lines 8 and 9, we have the recursive case where we call fibRec(n-1) and fibRec(n-2) and return the result of their sum. Inside the function, we have three base cases from lines 2 to 7. On line 1, we define a function called fibRec() that has one parameter n. Notice how much more elegant this function is? To use recursion to find the n th term of a Fibonacci sequence, we can use the function below: The base cases include the cases where n is negative (return -1), n is 1 (return 0) and n is 2 (return 1). In the case of a Fibonacci sequence, we have multiple base cases. Similar to all other recursion problems, we need to have a base case that returns the result and stops the recursion. This makes it a perfect case for using recursion. In turn, we can find the 5 th term by finding the 4 th and 3 rd terms and so on. For instance, we can find the 6 th term by finding the 5 th and 4 th terms. In the case of a Fibonacci sequence, we can find the n th term of the sequence by finding the (n-1) th and (n-2) th terms. Using recursionīesides using a for loop to calculate the n th term of a Fibonacci sequence, we can use recursion.Īs mentioned in a previous post, recursion is very useful when a problem can be solved by solving smaller instances of the same problem. If you run the code above, you’ll get 34 as the output. We call the function on line 18 (passing 10 as the argument) and use the print() function to print the result. We then return this value using a return statement on line 16. Next, we update the values of a and b so that they store the values of the most recent two numbers.Īfter we finish iterating through the for loop, result stores the n th term of the sequence. Inside the for loop, we calculate the Fibonacci value for the i th term by adding a with b. (Recall that range(x, y) gives us the numbers from x to y-1, not x to y) Next, we have a for loop that loops from i = 3 to i = n. Adding a and b then gives us the 7 th term in the sequence.īesides a and b, we also declare a variable called result and initialize it to 0 (line 11). When the loop runs again the next time, i becomes 7. For instance, when i equals 6, a and b will be updated to store the 5 th and 6 th terms in the sequence. At present, a and b store the first and second terms in the sequence respectively.Īs we iterate through the for loop later, a and b will be updated to store the preceding two numbers of subsequent numbers in the sequence. Inside the else case, we first assign 0 and 1 to the variables a and b respectively.Ī and b are used to store the preceding two numbers of any number in the sequence. If n is not negative, 0, 1 or 2, we move on to the else case (lines 8 to 16). If it is, we return the values 0 and 1 respectively. Next, we check if n is 1 (the first term) or 2 (the second term). Inside the function, we return -1 if n is invalid (i.e. For instance, if we want to find the 10 th term, n equals 10. In the example above, we have used five terms.Here, we first define a function called fibLoop() that has one parameter n. It is done until the number of words you want or requested by the user. The next word is produced using the second and third terms and does not use the first term. The third term is calculated by adding the first two words. In the example above, 0 and 1 are the first two concepts of the series. What is the Fibonacci Series? The Fibonacci series is a series of numbers formed by the addition of two increasing numbers in a series. We also discuss What is the Fibonacci Series and example of fibonacci series. In the second example discuss how to Plot the Fibonacci series in Python Programming using Matplotlib. We discuss two examples here in the first example you will learn how to print Fibonaaci series in Python Programming. In this article, you will learn how to write a Python program using the Fibonacci series using many methods. It is simply a series of numbers that start from 0 and 1 and continue with the combination of the previous two numbers. Python Program to print and plot the Fibonacci series The Fibonacci Sequence is a series of numbers named after the Italian mathematician, known as the Fibonacci.
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