The document discusses the Fibonacci sequence and rabbit problem. It begins with describing the rabbit problem posed by Fibonacci - where a pair of rabbits produces another pair each month, with new pairs becoming reproductive after 2 months. It then shows the sequence of pairs of rabbits each month, known as the Fibonacci sequence where each term is the sum of the previous two terms. Finally, it asks what the 10th and 15th terms are in the Fibonacci sequence and classifies several numerical sequences.

1. Ms. G. Martin

2. The Fibonacci posed the following problem:
The Rabbit Problem
Beginning with one pair of rabbits, how many rabbits will be born if
every month a pair of rabbits produces another pair; if the rabbits are
reproductive two months after their birth with the assumption that no rabbit
dies?

3. Mons Jan Feb Mar Apr May June Jul Aug Sept Oct Nov Dec
No. of
pairs
of
rabbits
each
month
of
2013
1 1 2 3 5 8 13 ____ ____ ____ ____ ____
The sequence 1, 1, 2, 3, 5, 8, 13, 21,…is called the Fibonacci sequence.
Observe that each term after the first is obtained by taking the sum of the two
preceding terms. The Fibonacci numbers were named after Leonardo of Pisa,
an Italian Mathematics.

4. The history of the Fibonacci sequence began in Pisa, Italy in 1202. The
infinite set of positive integers 1, 1, 2, 3, 5, 8, 13, 21, … appeared in the rabbit
problem in Leonardo Pisano Bigollo’s book the Liber Abaci.
What is the 10th term of the Fibonacci sequence? 15th?
The nth term of the Fibonacci sequence can be determined by taking the sum
of the two preceding terms.

5. Classify each sequence below as arithmetic sequence, geometric sequence,
harmonic sequence and Fibonacci sequence or neither.
1. 2, 2, 4, 6, 10, 16, …
2. 3, 3, 9, 18, 17, 27, …
3. 1, 1, 1, 1, 1, …..
4. -1, -1, -1, -1, -1, …
5. -1, 1, -1, 1, -1, …
6. 2, -1, -4, -7, -10, …
7.
1
5
,
1
9
,
1
12
,
1
16
,
1
19
, …
8.
1
4
,
1
7
,
1
10
,
1
13
,
1
16
, …