The male honeybee hatches from an unfertilized egg, while the female hatches from

a fertilized one. The “family tree” of a male honeybee is shown at the left, where

M represents male and F represents female. Starting with the male honeybee at the

top, and counting the number of bees in each generation, we obtain the following

numbers in the order shown.

Notice the pattern. After the first two terms (1 and 1), each successive term is

obtained by adding the two previous terms. This sequence of numbers is called the

Fibonacci sequence.

In this chapter, we study sequencesand sums of terms of sequences, known as

series.

1, 1, 2, 3, 5, 8

Sequences and Series

12.1 Sequences and

Series

12.2 Arithmetic

Sequences

12.3 Geometric

Sequences

12.4 The Binomial

Theorem

677

12

CHAPTER

M

M F

F

M F

M

F M F

F

F

F M F M F M F

8

5

3

2

1

1

F