The Fibonacci sequence is one of the most commonly found patterns in all of nature. The sequence starts with 0 and 1 , and then each term in the sequence is generated by adding the previous two terms. The first few terms in the sequence are 0,1,1 , 2, 3, 5, 8,13 , 21 , and 34. Numbers that appear in the sequence are called Fibonacci numbers.
a. Write a recursive algorithm in pseudo code to generate the Fibonacci sequence.
b. Write an iterative algorithm in pseudo code to generate the Fibonacci sequence.
c. Which algorithm would probably work better on a computer, and why?
d. Write an algorithm in pseudo code to test a number to see if it is a Fibonacci number.
e. Create an Alice world with a Count penguin and a Fibonacci penguin. Count penguin will simply start counting slowly when the world starts. The Fibonacci penguin will jump up and down and flap its wings while saying "Fibonacci, Fibonacci, (n) is Fibonacci!" when Count penguin says a number that is part of the Fibonacci sequence. The Fibonacci penguin should say the actual number in place of (n).