Intermediate Algebra (11th edition)

12.1 Sequences and Series

A finite sequence is a function with domain

while an infinite sequence has domain

.

Thenth term of a sequence is symbolized. A series is
an indicated sum of the terms of a sequence.

an

5 1, 2, 3,Á 6

5 1, 2,3,Án 6 ,

has general term

The corresponding series is the sum

1 +

1

2

+

1

3

+

1

4

+Á+

1

n

= a

n

i= 1

1

i

.

an=

1

n

1,.

1

2

,

1

3

,

1

4

,Á,

1

n

CONCEPTS EXAMPLES

12.2 Arithmetic Sequences

Assume that is the first term, is the nth term, and
dis the common difference.

Common Difference

nth Term

Sum of the First nTerms

or Sn

n

2

32 a 1  1 n 12 d 4

Sn

n

2

1 a 1 an 2

ana 1  1 n 12 d

dan 1 an

a 1 an Consider the arithmetic sequence

.

is the first term.

Use

(Any two successive terms could have been used.)

The tenth term is

Let

,or29.

The sum of the first ten terms can be found in either way.

= 155

= 155 = 51312

= 51312 = 514 + 272

= 512 + 292 = 514 + 9 # 32

S 10 =

10

2

S 10 = 32122 + 110 - 121324

10

2

12 +a 102

= 2 + 9 # 3

a 10 = 2 + 110 - 12132 n=10.

d= 5 - 2 = 3 a 2 - a 1.

a 1 = 2 a 1

2, 5, 8, 11,Á

12.3 Geometric Sequences

Assume that is the first term, is the nth term, and
ris the common ratio.

Common Ratio

nth Term

Sum of the First nTerms

Sn

a 111 rn 2

1 r

1 r 12

ana 1 rn^1

r

an 1

an

a 1 an Consider the geometric sequence

.

is the first term.

Use.

(Any two successive terms could have been used.)

The sixth term is

Let

The sum of the first six terms is

S 6 =

111 - 262

1 - 2

=

1 - 64

- 1

=63.

a 6 = 1121226 -^1 = 11225 =32. n=6.

a 4

r= a 3

8

4

= 2

a 1 = 1 a 1

1, 2, 4, 8,Á

CHAPTER 12 Summary 707

(continued)

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