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What is the Fibonacci sequence?
The Fibonacci sequence is a set of integers (the Fibonacci numbers) that starts with a zero, followed by a one, then by another one, and then by a series of steadily increasing numbers. The sequence follows the rule that each number is equal to the sum of the preceding two numbers.
The Fibonacci sequence begins with the following 14 integers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 …
Each number, starting with the third, adheres to the prescribed formula. For example, the seventh number, 8, is preceded by 3 and 5, which add up to 8.
The first two terms are 0 and 1. All other terms are obtained by adding the preceding two terms. This means to say the nth term is the sum of (n-1)th and (n-2)th term.
| # Program to display the Fibonacci sequence up to n-th term | |
| nterms = int(input("How many terms? ")) | |
| # first two terms | |
| n1, n2 = 0, 1 | |
| count = 0 | |
| # check if the number of terms is valid | |
| if nterms <= 0: | |
| print("Please enter a positive integer") | |
| # if there is only one term, return n1 | |
| elif nterms == 1: | |
| print("Fibonacci sequence upto",nterms,":") | |
| print(n1) | |
| # generate fibonacci sequence | |
| else: | |
| print("Fibonacci sequence:") | |
| while count < nterms: | |
| print(n1) | |
| nth = n1 + n2 | |
| # update values | |
| n1 = n2 | |
| n2 = nth | |
| count += 1 |
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