1. Recursive & Explicit Processes
Lesson 32

2. Objectives
HSF-BF.2: Write arithmetic and geometric sequences both Recursively and with and explicit formula, use them to model situations, and translate between the two forms.

3. Example; writing terms of a sequence
Write the first four terms of each sequence.
a. a1 = 5; ak = –2(ak-1) + 6
Solution:
a. The first five terms of the sequence given by
a1 = 5; ak = –2(ak-1) + 6
a1 = 5
a2 = -2(5) + 6 = -4
a3 = -2(-4) + 6 = 14
a4 = -2(14) + 6 = -22
a5 = -2(-22) + 6 = 50
5, -4, 14, -22, 50, …

4. Example; writing terms of a sequence
Write the first four terms of each sequence.
b. a1 = 1; ak = (ak-1)2 + 2
Solution:
b. The first five terms of the sequence given by
a1 = 1; ak = (ak-1)2 + 2
a1 = 1
a2 = (1)2 + 2 = 3
a3 = (3)2 + 2 = 11
a4 = (11)2 + 2 = 123
a5 = (123)2 + 2 = 15,131
1, 3, 11, 123, 15131, …

5. Example; Recursive Formula
c. Suppose you have the sequence:
5, 25, 125, 625, 3125, …
Write a recursive formula for the sequence.
Where does the sequence start?
Start at 5
What happens in the sequence?
Multiply by 5
Find a1.
a1 = 5
Find ak.
ak = 5(ak-1)

6. Example; Recursive Formula
d. Suppose you have the sequence:
2, 5, 8, 11, 14, …
Write a recursive formula for the sequence.
Where does the sequence start?
Start at 2
What happens in the sequence?
Add by 3
Find a1.
a1 = 2
Find ak.
ak = (ak-1) + 3

7. #32: Recursive & Explicit Processes
Questions?
Summarize Notes
Homework
Google Classroom
Quiz