Arithmetic Sequences as Functions

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Presentation transcript:

Arithmetic Sequences as Functions

Vocabulary Sequence – an ordered list of numbers that often form a pattern Term – each number in the sequence

Just two more vocab words! Arithmetic Sequence – this is a pattern in which the difference between consecutive terms is constant A pattern in which you add or subtract by the same number every time Common Difference – the constant difference in an arithmetic sequence

Describe the pattern in each sequence 5, 8, 11, 14, … The pattern is to “add 3” to the previous term! What are the next two terms? 14 + 3 = 17 and 17 + 3 = 20 So the next two terms are: 17 and 20

Describe the pattern in each sequence 400, 200, 100, 50, … The pattern is to multiply the previous term by ½ What are the next two terms? 50(1/2) = 25 and 25(1/2) = 12.5 So the next two terms are: 25 and 12.5

The common difference is…. Tell whether the sequence is arithmetic. If it is, identify the common difference. 19, 8, -3, -14, … YES!  The common difference is…. -11 WHY????

Tell whether the sequence is arithmetic Tell whether the sequence is arithmetic. If it is, identify the common difference. 10, -20, 40, -80 … No! 

Writing Sequences as Functions

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. 12 23 34 45 +11 +11 +11 The common difference is 11.

Arithmetic Sequences as Functions an = a1 + (n – 1)d Formula for the nth term = 12 + (n – 1)11 a1 = 12 and d = 11 = 12 + 11n – 11 Distributive Property = 11n + 1 Simplify. Answer: The function is an = 11n + 1.

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.