TOTAL MARK / 30 |

** Instructions:** Show all work for full marks. Add space if you need to.

Submit **ONE FILE** (PDF) under Unit 3 Assignment Folder in BrightSpace.

**Multiple Choice**

*Identify the choice that best completes the statement or answers the question.*

____ 1. If the first term of a sequence is 3 and the common difference is 4, what is the 23rd term in the sequence?

a. | 88 | c. | 95 |

b. | 87 | d. | 91 |

____ 2. What is the general term of the sequence: 6, 42, 294, 2058,14406, …

____ 3. If the 9th term in a geometric sequence is 45 927 and the common ratio is 3, then what is the first term?

a. | 7 | c. | 6 |

b. | 8 | d. | 9 |

____ 4. Find the next three terms of the sequence: 4, 11, 30, 67, …

a. | 125, 216, 343 | c. | 128, 219, 346 |

b. | 84, 246, 732 | d. | 246, 732, 2190 |

____ 5. Determine whether the sequence is geometric, arithmetic, neither with a defined general term, or neither with an undefined term.

8, 42, 76, 110, …

a. | Arithmetic | c. | Neither – Definable |

b. | Geometric | d. | Neither – Undefinable |

____ 6. Determine the sum of the arithmetic sequence: 5 + 18+ 31 + 44 + … +. 161.

a. | 1079 | c. | 996 |

b. | 1992 | d. | 2158 |

____ 7. Determine the sum of the geometric series 3 + 15 + 75 + 375 + … + 46 875.

a. | 58 593 | c. | 19 531 |

b. | 11 718 | d. | 292 968 |

____ 8. Expand the binomial (2*x* + 1)^{4}

**PART II Short Answer: **

*Show all steps for full marks*

9. Find the general term of the sequence 1, 1000, 10 000 000, 1 000 000 000 000 000, …

10. You are given a sequence: 1, 8, 4, 11, 7, 14, 10, 17, …

Describe in words how the sequence is obtained.

11. Calculate the sum of the series: –396 – 308 – 220 – 132 – … + 836.

12. Calculate the sum of the Geometric series

13. Expand and simplify the binomial power using Pascal’s Triangle

**Problem**

*Show all steps for full marks.*

14. The triangular numbers are the numbers in the sequence: 1, 3, 6, 10, 15, …

a) Determine the next three triangular numbers

b) Find the recursive formula for the sequence

c) Find the General form for the sequence

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