## Tuesday, May 29, 2007

### Scribe - Introduction to Sequences

Hello to everyone once again. Today I am scribing on both the morning class and the afternoon class. In the morning class we had a test on probability so there isn’t much I can talk about there. That’s it for the morning class. For the afternoon class, we started a new unit called sequences. Before we jumped into the work, Mr. K talked to us about fractal and showed us a video on it from www.youtube.com. If you would like to take a look at it, you can look to Mr. K’s post. After that we started off by taking a look at some problems:

Find the next 3 numbers in each sequence of numbers.

4, 7, 10, 13, , , … Answer: 4, 7, 10, 13, 16, 19, 22…

3, 6, 12, 24, , , … Answer: 3, 6, 12, 24, 48, 96, 192…

32, 16, 8, 4, , , … Answer: 32, 16, 8, 4, 2, 1, 0.5…

1, 1, 2, 3, 5, 8, 13, , , … Answer: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…

From each of these sequences, we can find out if they are geometric, arithmetic, or neither. Also if it is geometric, then we can find the common ratio and if it is arithmetic, then we can find the common difference. Here are some definitions to help you out:

Sequence: An ordered list of numbers that follow a certain pattern (or rule).

Arithmetic Sequence :(i) Recursive Definition: An ordered list of numbers generated by continuously adding a value (the common difference) to a given first term.
(ii) Implicit Definition: An ordered list of numbers where each number in the list is generated by a linear equation.

Common Difference (d):(i) The number that is repeatedly added to successive terms in an arithmetic sequence. (ii) From the implicit definition, d is the slope of the linear equation.

Geometic Sequence: (i) Recursive Definition: An ordered list of numbers generated by continuously multiplying a value (the common ratio) with a given first term.
(ii) Implicit Definition: An ordered list of numbers where each number in the list is generated by an exponential equation.

Common Ratio (r): (i) The number that is repeatedly multiplied to successive terms in a geometic sequence. (ii) From the implicit definition, r is the base of the exponential function.

Well that’s it for today and that just about covers everything that we went over today in class. Hopefully this helps you guys out a little bit more.

The next scribe is…Bertman!

Homework is exercise 45!