1. Standard and Learning Targets
F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*
SWBAT write arithmetic sequences explicitly
SWBAT write arithmetic sequences recursively

2. 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!

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

4. 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.

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

6. 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.

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

8. Quick Check

9. #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

10. #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

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

12. 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:

13. 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

14. 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

15. 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 = ???

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

17. Quick Check!

18. Independent Practice

19. 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