1 / 9

Recursive Rules for Special Sequences

Learn how to write recursive rules for special sequences using examples. Also, solve a multi-step problem and find the number of members over time.

timgraham
Download Presentation

Recursive Rules for Special Sequences

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. a. Beginning with the third term in the sequence, each term is the sum of the two previous terms. ANSWER So, a recursive rule is a1 = 1, a2 = 1, an= an – 2 + an–1. EXAMPLE 3 Write recursive rules for special sequences Write a recursive rule for the sequence. a. 1, 1, 2, 3, 5, . . . b. 1, 1, 2, 6, 24, . . . SOLUTION

  2. b.Denote the first term by a0 = 1. Then note that a1= 1= 1a0, a2= 2 = 2a1, a3= 6 = 3a2, and so on. ANSWER So, a recursive rule isa0 = 1, an= n an – 1. EXAMPLE 3 Write recursive rules for special sequences

  3. . Write a recursive rule for the number anof members at the start of the nth year. EXAMPLE 4 Solve a multi-step problem Music Service An online music service initially has 50,000 annual members. Each year it loses 20% of its current members and adds 5000 new members.

  4. . Find the number of members at the start of the 5th year. . Describe what happens to the number of members over time. EXAMPLE 4 Solve a multi-step problem SOLUTION STEP 1 Write a recursive rule. Because the number of members declines 20% each year, 80% of the members are retained from one year to the next. Also, 5000 new members are added each year.

  5. ANSWER A recursive rule isa1 = 50,000, an= 0.8an– 1 + 5000. EXAMPLE 4 Solve a multi-step problem

  6. Find the number of members at the start of the 5th year. Enter 50,000 (the value of a1) into a graphing calculator. Then enter the rule 0.8 Ans+ 5000to finda2. Press three more times to finda5. EXAMPLE 4 Solve a multi-step problem STEP 2

  7. what happens to the number of members over time. Continue pressing on the calculator. As shown at the right, after many years the number of members approaches 25,000. EXAMPLE 4 Solve a multi-step problem STEP 3 Describe

  8. ANSWER So, a recursive rule is a1 = 1, a2 = 2, an = (an – 2) (an – 1). for Examples 3 and 4 GUIDED PRACTICE 9. Write a recursive rule for the sequence. a. 1, 2, 2, 4, 8, 32, . . . .

  9. ANSWER The number of members stabilizes at about 16,667 members. for Examples 3 and 4 GUIDED PRACTICE 10. WHAT IF? In Example 4, suppose 70% of the member are retained each year. What happen to the number of member over time?

More Related