1. Silent Do Now (5 minutes)
Silent Do Now (5 minutes) * Before you begin, take out your homework (worksheet from last class)
Find the rate of change between (3,2) and (4,6).
There is a relationship between the number of the shape and the number of sides. Find the next shape in the sequence.

2. Agenda Review Do Now Track Exit Tickets Lesson on Sequences
Independent Practice
Exit Ticket

3. Sequences
Everyday a radio station asks a question for a prize of $150. If the fifth caller does not answer correctly, the prize money increased by $150 each day until someone correctly answers their question. Make a list of the prize money for a week from Monday to Friday if no one gets it right.
Fill out the chart on your paper accordingly!

4. Contest
Monday: $150 Tuesday: $300 Wednesday: $450 Thursday: $600 Friday: $750
These prize amounts form a sequence.

5. Important Definitions
Sequence: A function whose domain is a set of consecutive whole numbers. It can be specified by an equation or a rule. Arithmetic Sequence: a sequence that has a constant common difference.

6. Important Definitions (ctd.)
The values in the range are called the terms of the sequence. Domain: …....n Range: a1 a2 a3 a4….. An

7. Contest
a $150
a2 $300
Sequences can continue forever. We can calculate as many terms as we want as long as we know the rule or equation for an.
a3 $450
a4 $600
a5 $750
an represents a general term where n can be any number.

8. Example 1: Given the rule an = 6n – 4 , find the next term in the sequence.
2, 8, 14, 20, ___ ,___.

9. Quick Check

10. #1 Review an = 2n – 3 Find a1, a2, a3, a4, a5 a1 = -1 First Term
a2 = 1 Second Term
a3 = 3 Third Term
a4 = 5 Fourth Term
a5 = 7 Fifth Term

11. #2 Review an = -5n + 20 Find a1, a2, a3, a4, a5 a1 = First Term
a2 = Second Term
a3 = Third Term
a4 = Fourth Term
a5 = Fifth Term 15 10 5 -5

12. Arithmetic
Sequences
Explicit Formula
Recursive Formula
an = an-1 + d

13. Example 2: Write the rule for the nth term in the sequence
2, 6, 10, 14, Identify the first term: Identify the common difference between each of the values: Write the rule:

14. Review #1 a1 = 3 First Term a2 = 5 Second Term a3 = 7 Third Term
a4 = 9 Fourth Term
an = nth Term
What is the rule? an = ???
an= 3 + 2(n-1)
an= 3 + 2n – 2 = 2n + 1

15. Review #2 a1 = 2 First Term a2 = 6 Second Term a3 = 10 Third Term
a4 = 14 Fourth Term
an = nth Term
What is the rule? an = ???
an= 4n - 2

16. Review #3 a1 = 7 First Term a2 = 4 Second Term a3 = 1 Third Term
a4 = -2 Fourth Term
an = ?? nth Term
What is the rule? an = ???

17. Example 3: Find a specific term in a sequence
Find the 21st term in the sequence by writing a rule. 1, 10, 19, 28

18. Quick Check!

19. Independent Practice

20. Exit Ticket 1. Given the sequence: 3, 7, 11, 15, 19
Find the explicit formula for the nth term
Find the recursive formula.
Find the next two terms in the sequence
2. Find the 20th term in the sequence:
an = 4n - 5