Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

Normal Size Small Size show me how

Normal Size Small Size show me how

# Math1050 CH09

### Sequences

Side 1 | Side 2 |
---|---|

A sequence is a function whose domain is ___. | the set of positive integers |

The domain is also called the ___. | inputs |

We use ___ to represent the independent variable of a sequence. | n |

The outputs of a sequence are called ___. | terms |

The formula for the nth term is called the ___. | general term |

To represent the entire sequence we place ___ around the formula for the general (nth) term. | braces |

Factors such as (-1)^n+1, causes the signs of the terms to ___. | alternate |

A number multiplied by each successive smaller positive integer is called a ___. | factorial |

A factorial uses the symbol ___. | n! |

A factorial is defined as 0!=___, 1!=___, n!=___. | 1, 1, n(n-1)(...)(3)(2)(1) |

100!/98!=___. | (100)(99)=9900 |

(3)(2!)=___. | 3!=6 |

Assigning a value to the first term and listing the nth term is called a ___. | recursive formula |

The recursive formula, u_1 = 1, u_2 = 1, u_n = u_n-2 + u_n-1, is the ___ sequence. | Fibonacci |

In summation notation, k is the ___. It tells you ___. | index, where to start and end the sequence |

In summation notation, below the sigma tells you where to ___ the sequence and below tells you where to ___ it. | start, end |

In summation notation, to the right of the sigma is the ___. | sequence fomula |

Summation notation tells us the ___. | sum of the first n terms |

In summation notation, what does it mean when letters other than k are used? | Nothing. |

When the difference between successive terms of a sequence is always the same, the sequence is ___. | arithmetic |

An arithmetic sequence may be defined recursively as ___. | a_1 = a, a_n = a_n-1 + d |

In an arithmetic sequence d is ___. | the common difference (between each successive output) |

In an arithmetic sequence a is ___. | the first term |

The nth term is a way of saying ___. | any number in the sequence |

The formula for the nth term of an arithmetic sequence is ___. | a_n = a_1 + (n-1)d |

Using the formula for the nth term of an arithmetic sequence, a_41 = a_1 + (___)d. | 40 |

What are the 2 formulas for the sum of the first n terms of an arithmetic sequence? | n/2(2a_1 + (n-1)d) or n/2(a_1 + a_n) |

A sequence is geometric if the ___ of successive terms is always the same. | ratio |

A geometric sequence is defined recursively as ___. | a_1 = a, a_n = ra_n-1 |

In a geometric sequence the formula for r is ___. | r = a_n/a_n-1 (a term divided by the preceding term) |

For a geometric sequence, r is called the ___. | common ratio |

The nth term of a geometric sequence is defined by the formula a_n = ___. | (a_1)r^n-1 |

For a geometric sequence, the sum of the first n terms is defined by the formula S_n = ___. | a_1((1 - r^n)/(1-r)) |

For a geometric sequence, if a finite sum S_n approaches a number L as n approaches infinity, then the series ___. | converges |

For a converging series, we call L the ___. | sum of the geometric series |

If a geometric sequence doesn't converge then it ___. | diverges or is divergent |

For a converging series, r is always a ___. | proper fraction |

What is the series for the repeating decimal 0.999...? What is r? What is a_1? | 0.9 + 0.09 + 0.009 + ... or 9/10 + 9/100 + 9/1000 + ..., r = 1/10, a_1 = 9/10^k |

Created by:
drjolley