1. ©Evergreen Public Schools 2010 1 Learning Target I can write an equation of a geometric sequence in explicit form. What is explicit form for an arithmetic sequence?

2. ©Evergreen Public Schools 2010 2 LaunchLaunch From section 8.1 What are the domains of the L ( x ) and a ( x ) sequences?

3. ©Evergreen Public Schools 2010 3 LaunchLaunch Kingdom of Montarek DayPlan 1DayPlan 2DayPlan 3 111111 222324 3439316 632624361024 10512101968310262144 634611686018427390000154782969111048576 6492233720368547800001614348907124194304 From section 8.2 What are the domains of the plans?

4. ©Evergreen Public Schools 2010 4 LaunchLaunch What do you think is true about the domain of any sequence?

5. ©Evergreen Public Schools 2010 5 ExploreExplore

6. 6 Sequences a) 3, 6, 9, 12, 15, … b) 3, 6, 12, 24, 48, … 1.What do the sequences have in common? 2.How are they different? 3.Write an explicit rule with sequence notation for each.

7. ©Evergreen Public Schools 2010 7 Arithmetic Sequences L(x) = 2x + 1 and N(x) = 34 – 4x are arithmetic sequences. They have a constant rate of change. What is the rate of change of L(x) and N(x)?

8. ©Evergreen Public Schools 2010 8 Sequences The sequences in the Kingdom of Montarek problems are geometric sequences. They do not have a constant rate of change. What is the rate of change of each plan? Plan 1: 1, 2, 4, 8, 16, … Plan 2: 1, 3, 9, 243, … Plan 3: 1, 4, 16, 1024, …

9. ©Evergreen Public Schools 2010 9 Geometric Sequences The sequences that are generated by repeated multiplication are called geometric sequences. b)3, 6, 12, 24, 48, … from slide 7 is an example.

10. ©Evergreen Public Schools 2010 10 Geometric Sequences b)3, 6, 12, 24, 48, … from slide 7 is an example. Look for a pattern in ratio of consecutive terms Since the ratio is the same, we call it the common ratio.

11. ©Evergreen Public Schools 2010 11 Equations of Geometric Sequences We found the equations for the plans are Plan 1: Plan 2: Plan 3: b) What is the equation for 3, 6, 12, 24, …

12. ©Evergreen Public Schools 2010 12 Find next term and write equation with sequence notation. I 1, -10, 100, -1000, … II 5, 10, 20, 40, … III 4, 12, 36, 108, IV 64, 16, 4, 1, …

13. ©Evergreen Public Schools 2010 13 Find next term and write equation with sequence notation. III -243, -81, -27, -9, … IIIIV 4, 6, 9, 13.5

14. ©Evergreen Public Schools 2010 14 Write a formula to find the equations for geometric sequences r = common ratio In explicit form a n = n = term number In recursive form a n = and a n+1 = and

15. ©Evergreen Public Schools 2010 15 Team Practice problem numbers a n = 2 + 4(n – 1)

16. ©Evergreen Public Schools 2010 16 Debrief Complete the sequence organizer for geometric sequences.

17. ©Evergreen Public Schools 2010 17 5 3 1 2 4 Learning Target Did you hit the target? I can write an equation of a geometric sequence in explicit form. Rate your understanding of the target from 1 to 5. 5 is a bullseye!

18. ©Evergreen Public Schools 2010 18 Practice Practice 8.3A Geometric Sequences problems a n = 1 + 4(n – 1)