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*Then/Now You identified linear functions. (Lesson 3–1) Recognize arithmetic sequences. Relate...*

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You identified linear functions. (Lesson 3–1) • Recognize arithmetic sequences. • Relate arithmetic sequences to linear functions.

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Then/NowYou identified linear functions. (Lesson 31)Recognize arithmetic sequences.Relate arithmetic sequences to linear functions.

VocabularySequence : a set of numbers in a specific order

Terms : the numbers in the sequencearithmetic sequence: the difference between successive terms is a constantcommon difference: the difference between the terms

ConceptAn arithmetic sequence is a numerical pattern that increases or decreases at a constant rate call the common difference.Example: 3, 5, 7, Example: 33, 29, 25,

Example 1Identify Arithmetic SequencesA. Determine whether 15, 13, 11, 9, ... is an arithmetic sequence. Explain.

Example 1Identify Arithmetic Sequences

ABCExample 1 CYP AA. Determine whether 2, 4, 8, 10, 12, is an arithmetic sequence.

ABCExample 1 CYP B

Example 2Find the Next TermFind the next three terms of the arithmetic sequence 8, 11, 14, 17, .

ABCDExample 2 CYPFind the next three terms of the arithmetic sequence 58, 63, 68, 73.

ConceptThe nth term of an arithmetic sequence with first term a1 and common difference d is given by an = a1 + (n-1)d where n is a positive integer.

Example 3A. Write an equation for the nth term of the arithmetic sequence 1, 10, 19, 28, .Find the nth Term

Example 3C. Graph the first five terms of the sequence.Answer:The points fall on a line. The graph of an arithmetic sequence is linear.Find the nth Term

Example 3Find the nth TermD. Which term of the sequence is 172?

ABCDExample 3 CYP AMONEY The arithmetic sequence 2, 7, 12, 17, 22, represents the total number of pencils Claire has in her collection after she goes to her school store each week. A. Write an equation for the nth term of the sequence.

ABCDExample 3 CYP BMONEY The arithmetic sequence 2, 7, 12, 17, 22, represents the total number of pencils Claire has in her collection after she goes to her school store each week.B. Find the 12th term in the sequence.

ABExample 3 CYP CMONEY The arithmetic sequence 2, 7, 12, 17, 22, represents the total number of pencils Claire has in her collection after she goes to her school store each week. C. Which graph shows the first five terms of the sequence?

ABCDExample 3 CYP CMONEY The arithmetic sequence 2, 7, 12, 17, 22, represents the total number of pencils Claire has in her collection after she goes to her school store each week. D. Which term of the sequence is 97?

Example 4 AArithmetic Sequences as FunctionsNEWSPAPERS The arithmetic sequence 12, 23, 34, 45,... represents the total number of ounces that a bag weighs after each additional newspaper is added. A. Write a function to represent this sequence.

Example 4 bArithmetic Sequences as FunctionsNEWSPAPERS The arithmetic sequence 12, 23, 34, 45,... represents the total number of ounces that a bag weighs after each additional newspaper is added. B. Graph the function an = 11n + 1 and determine the domain. Answer:The domain of the function is the number of newspapers added to the bag {0, 1, 2, 3, 4}.The rate of change of the function is 11. Make a graph and plot the points.

ABCDExample 4SHIPPING The arithmetic sequence 22, 40, 58, 76, represents the total number of ounces that a box weighs after each additional bottle of salad dressing is added. A. Write a function to represent this sequence.

ABCDExample 4 CYP BSHIPPING The arithmetic sequence 22, 40, 58, 76, represents the total number of ounces that a box weighs after each additional bottle of salad dressing is added. B. Graph the function an = 18n + 4 and determine the domain of the sequence.