3. Patterns Comparing Functions Geometric Sequence s 100 200 300 400 500 100 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 Arithmetic Sequences Decipherin g Descriptio ns 200 Final Jeopardy

4. 100 Category 1 Answer 3, 6, 9, ___, ___,___

5. Answer 100 Category 1 3, 6, 9, 12, 15, 18

6. 200 Category 1 Answer The first term of a sequence is 5, and the recursive rule is a n = a n -1 – 6 What is the fourth term of the sequence?

7. Answer 200 Category 1 5, -1, -7, -13 The fourth term is -13.

8. 300 Category 1 Answer The first term of a sequence is 7, and the recursive rule is a n = 6a n -1 What is the fourth term of the sequence?

9. Answer 300 Category 1 7, 42, 252, 1512 The fourth term is 1512.

10. 400 Category 1 Answer The first term of a sequence is 5, and the recursive rule is a n = 2a n -1 + 2 What is the fourth term of the sequence?

11. Answer 400 Category 1 5, 12, 26, 54

12. 500 Category 1 Answer The first term of a sequence is 5, and the recursive rule is a n = 3a n -1 – 4 What is the fifth term of the sequence?

13. Answer 500 Category 1 5, 11, 29, 83, 245 The fifth term is 245.

14. 100 Category 2 Answer Write the recursive rule if a 1 = 10 d = 3

15. Answer 100 Category 2 Write the recursive rule if a 1 = 10 d = 3 a n = a n-1 + 3

16. 200 Category 2 Answer Write the explicit/closed rule if a 1 = 15 d = -2

17. Answer 200 Category 2 Write the rule if a 1 = 15 d = -2 a n = 15 – 2(n-1) a n = -2n + 17

18. 300 Category 2 Answer Write the first 5 terms for a n =6+5n

19. Answer 300 Category 2 Write the first 5 terms for a n =6+5n 11, 16, 21, 26, 31

20. 400 Category 2 Answer Find a 20 for 10, 6, 2, -2...

21. Answer 400 Category 2 Find a 20 for 10, 6, 2, -2… a n =14 - 4n so a 20 = 14 - 4(20) = -66

22. 500 Category 2 Answer Find the closed and recursive rules for 7, 11, 15, 19, …

23. Answer 500 Category 2 a 1 = 7 d = 4 Recursive : a n = a n-1 + 4 Closed : a n = 7 + 4(n – 1)

24. 100 Category 3 Answer Which function has a greater rate of change between [2,4]?

25. Answer 100 Category 3 Function m: ROC=slope=25 Function o: (120 – 60)/(4 – 2) =30 Function O has a greater rate of change.

26. 200 Category 3 Answer Which function has a greater y- intercept?

27. Answer 200 Category 3 Which function has a greater y- intercept?

28. 300 Category 3 Answer Which function has a smaller y- intercept?

29. Answer 300 Category 3 Which function has a smaller y- intercept?

30. 400 Category 3 Answer Which function has a greater rate of change between [1,3]?

31. Answer 400 Category 3 Which function has a greater rate of change between [1,3]?

32. 500 Category 3 Answer Which function has a smaller rate of change between [2,4]?

33. Answer 500 Category 3

34. 100 Category 4 Answer Write the recursive rule if r = 6 and a 1 =7

35. Answer 100 Category 4 Write the rule if r = 6 and a 1 =7 a n = 6a n -1

36. 200 Category 4 Answer Write the closed rule for 2, 10, 50, 250...

37. Answer 200 Category 4 Write the rule for 2, 10, 50, 250… a 1 =2 r = 5 a n = 2(5) n-1

38. 300 Category 4 Answer Write the explicit/closed rule for 360,120, 40...

39. Answer 300 Category 4 Write the rule for 360,120, 40… a n = 360(1/3) n-1

40. 400 Category 4 Answer Write out the first 5 terms if a n = 3(2) n-1

41. Answer 400 Category 4 Write out the first 5 terms if a n = 3(2) n-1 3, 6, 12, 24, 48

42. 500 Category 4 Answer Write the explicit and recursive rules for 6, 18, 54, 162, …

43. Answer 500 Category 4 a 1 = 6r = 3 Recursive: a n = 3a n-1 Closed: a n = 6(3) n-1

44. 100 Category 5 Answer You just graduated college and are thinking about how to pay off your loan of $50,000. After paying $10,000 to the bank, you decide to pay $400 each month. Write an equation to model this situation. What is the rate of change?

45. Answer 100 Category 5 Y=-400x+40000 ROC: -400

46. 200 Category 5 Answer You just graduated college and are thinking about how to pay off your loan of $50,000. After paying $10,000 to the bank, you decide to pay 6.5% each month. Write an equation to model this situation. What is the rate of decay?

47. Answer 200 Category 5 Y=40000(1-0.065) x Y=40000(0.935) x Rate of decay=0.065 or 6.5%

48. 300 Category 5 Answer You just graduated college and are thinking about how to pay off your loan of $50,000. After paying $10,000 to the bank, you decide to pay $400 each month. How much will you have left to pay on the 12 th month?

49. Answer 300 Category 5 Y=-400(12)+40000 Y=35200 $35,200

50. 400 Category 5 Answer You just graduated college and are thinking about how to pay off your loan of $50,000. After paying $10,000 to the bank, you decide to pay 6.5% each month. If an equation was written to model this situation, what would the y- intercept be?

51. Answer 400 Category 5 Y=40000(1-0.065) 0 Y=40000

52. 500 Category 5 Answer You just graduated college and are thinking about how to pay off your loan of $50,000. After paying $10,000 to the bank, you decide to pay 6.5% each month. Your friend also owes $50,000. After paying $10,000 to the bank, your friend decides to pay $500 each month. Will you or your friend have a smaller average rate of change between [0,3]?

53. Answer 500 Category 5 You: f(x)=40000(1-0.065) x f(0)=40000(1- 0.065) 0 =40000 f(3)=40000(1- 0.065) 3 =32696.02 ROC: (32696.02-40000)/(3- 0)=-2434.66 Your Friend: f(x)=-500x + 40000 ROC: -500

54. Double Jeopardy Fill in the blank for the geometric sequence: 2, ___, ___, ___,1250 Answer

55. Double Jeopardy Answer 2,,,,1250 10,50,250

56. Final Jeopardy Write all eight equations I told you to memorize for the test. Answer

57. Final Jeopardy