Name: ____________________________
Date: ___________________
Period: _______
Algebra II: Fibonacci Sequence
Leonardo Bonacci, known as Fibonacci, was an Italian merchant and mathematician,
who published this problem in the 13th century in his book, Liber Abaci.
He asked how fast rabbits breed in ideal circumstances. He imagined a newly-born
pair of rabbits, one male and one female placed in a field and made the following
assumptions about the mating habits of rabbits:



Rabbits mate at exactly the age of one month and mate every month after that.
Rabbits always have litters of exactly one male and one female.
Rabbits never die.
Hint to problem: Only the rabbits that have been alive for two months or more will give birth to a new
pair of rabbits. How many pairs of those rabbits will there be? These new pairs along with the pairs alive
during the previous month, will give you the number of pairs there are at the beginning of any given month.
Complete the chart to help you calculate how many adult rabbits, how many new rabbits, and how many
total rabbits there will be after 12 months (1 year):
(Some of the chart is already filled out for you!)
Month
Number of adult
rabbits
(by pair)
Number of new
matings
Number of new
baby rabbits
(each adult pair has
one pair of babies)
Total rabbit
pairs
1
0
0
one pair
1
2
1
original pair mates
0
1
3
1 (original pair)
1 (new babies)
1
2
4
1
original pair has
another pair of babies
3
1
5
6
3
7
3
8
3
8
5
55
9
13
13
10
11
12
(after one year)
55
144
Name: ____________________________
Date: ___________________
Period: _______
Mathematically, the Fibonacci number starts with the “seed” 0,1.
We will go ahead and start with 1, 1 and use the same process to obtain the Fibonacci sequence.
Add 1 + 1 together to get the next number, 2.
Add the new number, 2, to the previous number, 1, to get the next number.
1) Continue the pattern:
0, 1, 1, 2, 3, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____, …
2) What relationship is there with the “rabbit” problem?
3) Which Fibonacci numbers are even? Can you predict where the even Fibonacci numbers will
appear?
4) Which Fibonacci numbers are multiples of 3? Can you predict where they will appear next?