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

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

Vocabulary Sequence : a set of numbers in a specific order Terms : the numbers in the sequence arithmetic sequence: the difference between successive terms is a constant common difference: the difference between the terms

Concept An 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 1 Identify Arithmetic Sequences A. Determine whether –15, –13, –11, –9,... is an arithmetic sequence. Explain.

Example 1 Identify Arithmetic Sequences B. Determine whether is an arithmetic sequence. Explain.

A.A B.B C.C Example 1 CYP A A. Determine whether 2, 4, 8, 10, 12, … is an arithmetic sequence.

A.A B.B C.C Example 1 CYP B B. Determine whether … is an arithmetic sequence.

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

A.A B.B C.C D.D Example 2 CYP Find the next three terms of the arithmetic sequence 58, 63, 68, 73….

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

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

Example 3 C. 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 3 Find the nth Term D. Which term of the sequence is 172?

A.A B.B C.C D.D Example 3 CYP A MONEY 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.

A.A B.B C.C D.D Example 3 CYP B MONEY 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.

A.A B.B Example 3 CYP C MONEY 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?

A.A B.B C.C D.D Example 3 CYP C MONEY 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 A Arithmetic Sequences as Functions NEWSPAPERS 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 b Arithmetic Sequences as Functions NEWSPAPERS 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 a n = 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.

A.A B.B C.C D.D Example 4 SHIPPING 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.

A.A B.B C.C D.D Example 4 CYP B SHIPPING 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 a n = 18n + 4 and determine the domain of the sequence.