Algebra 2 - Formulas for Chapter 12



Chapter 9 Review: Sequences and Series Name: ________________________________

|Skill |I Got this! |Eh, I need help. |I have NO idea! |

|Determine if something is Arithmetic or Geometric | | | |

|Find the value of the nth term | | | |

|Use the explicit formula | | | |

|Use the recursive formula | | | |

|Find the arithmetic/geometric means | | | |

|Understand the difference between a sequence and a series | | | |

|Use summation notation | | | |

|Use the formulas to find infinite and finite series. | | | |

Are these sequences arithmetic, geometric, or neither?

1. [pic], 1, [pic], 2, [pic],…

2. 16, 14, 11, 6, 3

3. 16, 25, 36, 49, . . .

4. 20, 10, 5, 2.5, 1.25

5. 1, -2, -5, -8, -11

Write the first 4 terms of each sequence:

6. [pic]

7. [pic]

8. [pic]

9. [pic]

10. Arithmetic sequence with [pic], [pic]

Write the rule for each sequence AND then find the value of the tenth term.

11. Arithmetic with [pic] and [pic]

12. Geometric with [pic], r = 5

13. Arithmetic with [pic], d = 5

14. Arithmetic with [pic] and [pic]

15. geometric with [pic], [pic]

Determine whether the sequence is geometric or arithmetic, then find the rule for the nth term.

16. -3, -1, 1, 3, 5, . . .

17. 0.3, 0.6, 1.2, 2.4,….

18. 7, -35, 175, -875,…

Find the sum of the first 12 terms of each series.

21. 5, -14, 39.2, -109.76,…

22. 8, 12, 16, 20, . . .

23. 4, 24, 144, 864,…

24. -30, -24, -18, -12, . . .

Answer these miscellaneous questions:

25. Find three arithmetic means between 9 and 601

26. Find two geometric means between -104 and -13

27. [pic]

28. [pic]

29. [pic]

30. [pic]

31. [pic]

32. [pic]

33. [pic]

34. Find the sum of the infinite series -16, 8, -4, 2, . . .

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