PATTERNS The following are the first nine Fibonacci numbers.
1, 1, 2, 3, 5, 8, 13, 21, 34, ...
a. Make a conjecture about each of the Fibonacci numbers after the first two.
Each number in the sequence is the sum of the previous two numbers in the sequence.
The next consecutive integer, beginning with 1, is added to the previous number in the sequence.
Each number in the sequence is multiplied by 2, then 1 is subtracted from the product.
Find the difference between the square of each number and the next consecutive odd integer to get the
next number.
b. Write the next three numbers in the pattern.
1, 1, 2, 3, 5, 8, 13, 21, 34,
c. Research to find and explain a real-world example of this pattern.