11.111.1Arithmetic SequencesArithmetic Sequences

VocabularyVocabularysequence term

arithmetic sequence

each term after the first is found

by addin consg a tant

each number

in a sequencelist of numbers in

a particular order

Example 1

Find the next four terms of the

arithmetic sequence.

Example 2

8, 6, 4,... 5,3,1,...

nnthth term of an arithmetic sequence term of an arithmetic sequence

1 ( 1)na a n d

generalizes the pattern in the way terms

of an arithmetic sequence are formed

n :

na :

d :

1a :

Example 3a

Part b

Construction The table below shows typical costs fora construction company to rent a crane for one, two,three, or four months. Assuming that the arithmeticsequence continues, how much would it cost to rentthe crane for 24 months?

MonthsMonths Cost($)Cost($)

11 75,00075,000

22 90,00090,000

33 105,000105,000

44 120,000120,000

How much would it cost to rentthe crane for 8 months?

Example 4

thWrite an equation for the n term

of the arithmetic sequence.

Example 5

8, 6, 4,... 5,3,1,...

Example 6

Find the indicated term

of the arithmetic sequence.

Example 7

1 3, 5, 24a d n

1 5, 7, 13a d n

68 is a term in an arithmetic sequence. If 68 is a term in an arithmetic sequence. If a a11 = 5 and d = 3, which term is it? = 5 and d = 3, which term is it?

Example 8

VocabularyVocabularyarithmetic means

the terms between any two nonsuccessive

terms of an arithmetic sequence

Example 9

Find the 3 arithmetic means

between the values given.

Example 10

21 and 45 13 and 25