1. WARM UP/GO OVER IT: 15 MINUTES ANNOUNCEMENTS: 1 MINUTE HOMEWORK: 10 MINUTES GEOMETRIC SEQUENCES: 30 MINUTES CLASS WORK: 20 MINUTES MIDTERM RETURN/CLOSURE: 10 MINUTES AFM Unit 5 – Sequences and Series

2. Warm Up 1. Write the explicit and recursive formula for the following sequences: 4, 21, 38,… -4.5, -9.5, -14.5,… 2. Find the 6 th term of each of the following sequences, and tell whether the formula given is explicit or recursive. a 1 = 10, a n = a n – 1 – 7 a n = 15n – 9 3. Find the common difference of the arithmetic sequence for which a 1 = 75 and a 38 = 56.5

3. Announcements You have until THIS (Friday) afternoon to complete any and all make up work for this quarter. This includes finishing your midterm and make up tests. I will be here today after school. You will get your midterm grades back at the end of the period. We will stop about 6 minutes before the bell rings so you can get them back and look through them.

4. HOMEWORK: Check your answers 1. Yes, d = -3 2. Yes, d = -20 3. Yes, d = -30 4. Yes, d = -10 5. Yes, d = -2 6. Yes, d = 5 7. -4, 3, 10, 17, 24 and 227 8. -35, -135, -235, -335, -435 and -3835 9. -9.2, -11.3, -13.4, -15.5, -17.6 and -63.8 10. 1.875, 2.375, 2.875, 3.375, 3.875 and 12.875

5. Homework – You give ME the answers!

8. Yesterday: Arithmetic Sequences What do you remember about arithmetic sequences? What was the formula for the recursive formula? What was the formula for the explicit formula?

9. Today: Geometric Sequences Geometric Sequences – a few examples below to see if you can figure out what makes a geometric sequence a geometric sequence

10. Geometric Sequence The ratio between successive terms is constant. In other words…Each term is multiplied or divided by the same number. Example: -3, -15, -75, -375

11. Are the following sequences geometric?

12. Common Ratio The number that each term is multiplied or divided by to get the next term. Represented by the variable “r” To find it: divide any term by the previous term. Example: What is the common ratio of the sequence below?

13. Find the common ratios of the sequences below. 8, -2, 1/2 … 4, 11, 30.25… W + 3, 2w + 6, 4w + 12…

14. Find the common ratio and use it to generate the next 4 terms of each sequence below. - ¼, ½, -1, … 0.5, 0.75, 1.125, …

15. Recursive Formula Gives you… The first term (a 1 ) What to multiply the previous term by Remember, a n – 1 means “the one that came before it”

16. Geometric Recursive Formula a n = a n – 1 r

17. Generate the first 4 terms of the sequences given by the formulas below: a 1 = 8, a n = a n – 1 2.5 a 1 = 2x, a n = a n – 1 5

18. Recursive  Explicit Let’s say you have a geometric sequence where a 1 = 3 and r = 4 first terma1a1 a1a1 a1a1 3 Second terma2a2 Third term Fourth term Fifth term Sixth term

19. GEOMETRIC EXPLICIT FORMULA a n = a 1 r n – 1

20. Writing Formulas Write an explicit and recursive formula for finding the nth term of the geometric sequence below. 2, 25, 312.5,…..

21. You try the next 3. 36, 12, 4,… -2, 10, -50,… 4, 8, 16,…

22. Nth terms Find the 27th term of the geometric sequence 189, 151.2, 120.96…

23. You try two. Find a 9 for 60, 30, 15… Find a 6 for 7, 14, 28,…

24. Arithmetic vs. Geometric

25. Practice Time Complete the problems on the worksheet I give you. You may work with your neighbors. Whatever you do not finish is homework!

26. Homework Finish class work!

27. Midterm Return Each part of each question was worth an equal amount. There was no partial credit. Your answer was either right or wrong. That means there were 58 total points. Your total correct out of 58 is where I got the percentage.