Download presentation

Presentation is loading. Please wait.

Published byGiselle Lugg Modified over 2 years ago

1
11.5 Recursive Rules for Sequences p. 681

2
Explicit Rule A function based on a term’s position, n, in a sequence. All the rules for the nth term that we’ve been working with are explicit rules; such as a n =a 1 r n-1.

3
Recursive Rule Gives the first term(s) of a sequence and an equation that relates the given term(s) to the next terms in the sequence. For example: Given a 0 =1 and a n =a n-1 -2 The 1 st five terms of this sequence would be: a 0, a 1, a 2, a 3, a 4 OR 1, -1, -3, -5, -7

4
Example: Write the 1 st 5 terms of the sequence. a 1 =2, a 2 =2, a n =a n-2 -a n-1 a 3 =a 3-2 -a 3-1 =a 1 -a 2 =2-2=0 a 4 =a 4-2 -a 4-1 =a 2 -a 3 =2-0=2 a 5 =a 5-2 -a 5-1 =a 3 -a 4 =0-2=-2 2, 2, 0, 2, -2 1 st term 2 nd term

5
Example: Write the indicated rule for the arithmetic sequence with a 1 =15 and d=5. Explicit rule a n =a 1 +(n-1)d a n =15+(n-1)5 a n =15+5n-5 a n =10+5n Recursive rule (*Use the idea that you get the next term by adding 5 to the previous term.) Or a n =a n-1 +5 So, a recursive rule would be a 1 =15, a n =a n-1 +5

6
Example: Write the indicated rule for the geometric sequence with a 1 =4 and r=0.2. Explicit rule a n =a 1 r n-1 a n =4(0.2) n-1 Recursive rule (*Use the idea that you get the next term by multiplying the previous term by 0.2) Or a n =r*a n-1 =0.2a n-1 So, a recursive rule for the sequence would be a 1 =4, a n =0.2a n-1

7
Write a recursive rule for the sequence 1,2,2,4,8,32,…. First, notice the sequence is neither arithmetic nor geometric. So, try to find the pattern. Notice each term is the product of the previous 2 terms. Or, a n-1 *a n-2 So, a recursive rule would be: a 1 =1, a 2 =2, a n = a n-1 *a n-2

8
Example: Write a recursive rule for the sequence 1,1,4,10,28,76. Is the sequence arithmetic, geometric, or neither? Find the pattern. 2 times the sum of the previous 2 terms Or 2(a n-1 +a n-2 ) So the recursive rule would be: a 1 =1, a 2 =1, a n = 2(a n-1 +a n-2 )

9
Assignment

Similar presentations

OK

Lesson 3A: Arithmetic Sequences Ex 1: Can you find a pattern and use it to guess the next term? A) 7, 10, 13, 16,... B) 14, 8, 2, − 4,... C) 1, 4, 9,

Lesson 3A: Arithmetic Sequences Ex 1: Can you find a pattern and use it to guess the next term? A) 7, 10, 13, 16,... B) 14, 8, 2, − 4,... C) 1, 4, 9,

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on rational numbers for class 8th Ppt on systematic layout planning Ppt on earth movements and major landforms in africa Ppt on sports day Ppt on otto cycle free download Ppt on limits and continuity of several variables Ppt on cold chain storage of food Kid after dentist appt on your birthday Quiz ppt on india Ppt on companies act 2013 vs companies act 1956