Intermediate Algebra (11th edition)

706 CHAPTER 12 Inverse, Exponential, and Logarithmic Functions

12.1

infinite sequence
finite sequence
terms of a sequence
general term
series
summation notation

index of summation

arithmetic mean (average)

12.2

arithmetic sequence

(arithmetic progression)

common difference

12.3

geometric sequence

(geometric progression)

common ratio

annuity

ordinary annuity

payment period

future value of an annuity

term of an annuity

12.4

Pascal’s triangle

binomial theorem (general

binomial expansion)

KEY TERMS

nth term of a

sequence

a summation notation

n

i 1

ai

an sum of first nterms
of a sequence
limit of as ngets
larger and larger

liman an

n:ˆ

Sn

sum of an infinite

number of terms

n! nfactorial

a

ˆ

i 1

ai

binomial coefficient

(combinations of n

things taken rat a time)

nCr

NEW SYMBOLS

1.An infinite sequenceis
A.the values of a function
B.a function whose domain is the
set of positive integers
C.the sum of the terms of a function
D.the average of a group of
numbers.

2.A seriesis
A.the sum of the terms of a
sequence
B.the product of the terms of a
sequence
C.the average of the terms of a
sequence
D.the function values of a sequence.

3.An arithmetic sequenceis a
sequence in which
A.each term after the first is a
constant multiple of the
preceding term

B.the numbers are written in a

triangular array

C.the terms are added

D.each term after the first differs

from the preceding term by a

common amount.

4.A geometric sequenceis a sequence

in which

A.each term after the first is a

constant multiple of the

preceding term

B.the numbers are written in a

triangular array

C.the terms are multiplied

D.each term after the first differs

from the preceding term by a

common amount.

5.The common differenceis

A.the average of the terms in a

sequence

B.the constant multiplier in a

geometric sequence

C.the difference between any two

adjacent terms in an arithmetic

sequence

D.the sum of the terms of an

arithmetic sequence.

6.The common ratiois

A.the average of the terms in a

sequence

B.the constant multiplier in a

geometric sequence

C.the difference between any two

adjacent terms in an arithmetic

sequence

D.the product of the terms of a

geometric sequence.

TEST YOUR WORD POWER

See how well you have learned the vocabulary in this chapter.

ANSWERS

SUMMARY

CHAPTER 12

1.B; Example:The ordered list of numbers 3, 6, 9, 12, 15 is an infinite sequence.

2.A; Example: written in summation notation as is a series.

3.D; Example:The sequence 2, 7, 12, 17 is arithmetic.
4.A; Example:The sequence 1, 4, 16, 64, 256 is geometric.
5.C; Example:The common difference of the arithmetic sequence in Answer 3 is 5, since and so on.

6.B; Example:The common ratio of the geometric sequence in Answer 4 is 4, since^41 =^164 =^6416 =^25664 =4.

2 - 1 - 32 =5, 7- 2 =5,

,Á

• 3, ,Á

a

5

i= 1

3 + 6 + 9 + 12 +15, 3 i,

,Á

706 CHAPTER 12 Sequences and Series