4.7 – Sequences and Functions

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

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

Tell whether the sequence is arithmetic 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! 

Exit Slip: Get out a half sheet of paper. Answer the following questions all by yourself.

Exit Slip: Describe the pattern and give the next two terms: 1, 3, 9, 27, … Write an arithmetic sequence with 5 terms that has a common difference of 10.