Summary: A teacher's guide for lecturing on arithmetic and geometric sequences.

The in-class assignment does not need any introduction. Most of them will get the numbers, but they may need help with the last row, with the letters.

After this assignment, however, there is a fair bit of talking to do. They have all the concepts; now we have to dump a lot of words on them.

A “sequence” is a list of numbers. In principal, it could be anything: the phone number 8,6,7,5,3,0,9 is a sequence.

Of course, we will not be focusing on random sequences like that one. Our sequences will usually be expressed by a formula: for instance, “the xxxnth terms of this sequence is given by the formula *function* *sequence*, xxxn must be a positive integer; you do not have a “minus third term” or a “two-and-a-halfth term.”

The first term in the sequence is referred to as

The number of terms in a sequence, or the particular term you want, is often designated by the letter

Our first sequence adds the same amount every time. This is called an *arithmetic sequence*. The amount it goes up by is called the *common difference*

If I want to know all about a given arithmetic sequence, what do I need to know? Answer: I need to know

OK, so if I *have*

Time for some more words. A *recursive definition* of a sequence defines each term in terms of the previous. For an arithmetic sequence, the recursive definition is *explicit definition* defines each term as an absolute formula, like the

Our second sequence multiplies by the same amount every time. This is called a *geometric sequence*. The amount it multiplies by is called the *common ratio * (since it is the ratio of any two adjacent terms).

Find the recursive definition of a geometric sequence. (Answer:

Question: How do you make an arithmetic sequence go *down*? Answer:

Question: How do you make a geometric series go down? Answer:

“Homework: Arithmetic and Geometric Sequences”

Comments:"This is the "teacher's guide" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing […]"