Math rocks



Sequences and Series

Module Quiz: B

For 1–2, use the table to write an explicit rule and a recursive rule for the sequence.

|n |0 |1 |2 |3 |4 |5 |

|f(n) |7 |11 |15 |19 |23 |27 |

explicit:

recursive:

|n |0 |1 |2 |3 |... |

|f(n) |0.12 |0.36 |1.08 |3.24 |... |

explicit:

recursive:

3. A new store has sales of $2000 its first week, and its sales grow by 2% each week. Choose True or False for each statement about the geometric series that describes the store’s total sales the first

6 weeks.

A a ’ $2000 [pic] True [pic] False

B r ’ 0.02 [pic] True [pic] False

C n ’ 6 [pic] True [pic] False

D S(n) ’ $12,245 [pic] True [pic] False

4. Complete the table of values for the sequence f(n) ’ −2 + 3n, [pic]Then draw the graph of the sequence.

|n |1 |2 |3 |4 | | |

|f(n) | | | | | | |

[pic]

For 5–7, consider a rental property with a 5-year lease. The annual rent is $62,000 the first year and increases by 3% each additional year of the lease.

5. Write an explicit rule that describes the rent after n years.

6. Write a recursive rule that describes the rent after n years.

7. What is the rent for the fifth year?

Sequences and Series

Module Quiz: B

8. A geometric series begins with 500 and decreases by 15% successively. Choose True or False for each statement about the series.

A The common ratio is 1.15.

[pic] True [pic] False

B In the sum formula, a ’ 500 and

r ’ 0.85.

[pic] True [pic] False

C The sum, if the series has 5 terms, is 1,854 (rounded to the nearest integer).

[pic] True [pic] False

D The sum, if the series has 9 terms, is 2425 (rounded to the nearest integer).

[pic] True [pic] False

For 9–11, given the recursive rule for an arithmetic sequence, write the explicit rule and complete the table of values.

9. f(1) ’ 8 and f(n) ’ f(n − 1) + 7 for [pic]

|n |2 |3 |4 |5 |6 |7 |

|f(n) | | | | | | |

10. f(0) ’ 15 and f(n) ’ f(n − 1) − 3 for [pic]

|n |1 |2 |3 |4 |5 |6 |

|f(n) | | | | | | |

11. f(0) ’ −4 and f(n) ’ f(n − 1) + 5 for [pic]

|n |1 |2 |3 |4 |5 |6 |

|f(n) | | | | | | |

12. Complete the table of values for the sequence [pic] [pic] Then draw the graph of the sequence.

|n |0 |1 |2 |3 |4 |... |

|f(n) | | | | | |... |

[pic]

For 13–15, determine the number of terms that are included in each geometric series and find the sum of the series. Round the sum to the nearest whole number if necessary.

13. 2 + 8 + 32 + ... + 2048

Number of terms:

Sum:

14. −20 − 10 − 5 − ... − [pic]

Number of terms:

Sum:

15. 162 + 54 + 18 + ... + [pic]

Number of terms:

Sum:

11. 8

12. [pic]

13. 2

14. [pic] [pic]

15. B

16. C

17. A

18. 14

19. 4; [pic] is extraneous

20. [pic]

21. [pic]

22. 26 ft

MODULE 12 Sequences and Series

Module 12 Quiz: B

1. explicit: f(n) ’ 7 + 4n; recursive: f(0) ’ 7 and f(n) ’ f(n − 1) + 4 for [pic]

2. explicit: f(n) ’ 0.12(3)n; recursive: f(0) ’ 0.12 and f(n) ’ 3f(n − 1) for [pic]

3. A True B False C True D False

4. [pic]

5. [pic]

6. [pic]; f(1) ’ 62,000

7. $69,781.55

8. A False B True C True D False

9. f(n) ’ 8 + 7(n − 1)

n |2 |3 |4 |5 |6 |7 | |f (n) |15 |22 |29 |36 |43 |50 | | 10. f(n) ’ 15 − 3n

n |1 |2 |3 |4 |5 |6 | |f (n) |12 |9 |6 |3 |0 |−3 | | 11. f(n) ’ −4 + 5n

[pic]

12.

[pic]

13. Number of terms: 6; Sum: 2730

14. Number of terms: 8; Sum: −40

15. Number of terms: 7; Sum: 243

Module 12 Quiz: Modified

1. A

2. C

3. B

4. C

5. [pic]

-----------------------

module

12

1.

2.

module

12

n |1 |2 |3 |4 |5 |6 | |f (n) |1 |6 |11 |16 |21 |26 | |

n |0 |1 |2 |3 |4 |... | |f (n) |12 |6 |3 |1.5 |0.75 |... | |

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download