## Geometric Sequence

### Xiuqing LiEscambia County Schools

#### Description

Students will learn the geometric sequence and find the sum of an geometric sequence.

#### Objectives

Applies special number relationships such as sequences and series to real-world problems.

#### Materials

- Transparency (see attached file)
- Marker
- Worksheet, one per student (see attached file)

#### Preparations

1. Prepare the transparency ahead of time--should contain definition and examples.
2. Prepare a copy of a worksheet for each student.

#### Procedures

Note: This lesson only covers geometric sequences and series for SSS MA.A.5.4.1.

1. PROMPT: "Let's say, I would give you an 'A; in the class if you would give my \$0.01, but the it would go up geometrically. Day 2, you'd give me \$0.02, and day 3, \$0.04, and so on and so forth for 30 days. How many of you would take that challenge?" Some students may raise their hand. PROMPT: "If so, then can you calculate how much you'd give me on the 30th day and over the entire 30 day period?" It is expected that students will have some difficulty in solving this problem.

2. PROMPT: "The above example is called a geometric sequence."

3. Definition of a geometric sequence (see attached file).

4. Definition to find the general term of a geometric sequence (see attached file).

5. Find the nth term (see attached file).

6. PROMPT: "Let's do a few examples before attempting our problem." Do examples on transparency.

7. Attempt the first part of the problem in regards to giving money \$0.01 on first day, \$0.02 on second day, and figure out how much the student would pay on Day 30.

8. PROMPT: "Now, that we have figured out how much you have to pay me on Day 30. Let's figure out how much you would have to pay me for all 30 days. But before doing so, you have to learn the formula for the sum of a geometric sequence."

9. Definition of the sum of a geometric sequence. (Definition is found on the transparency).

10. Solve a few sample problems from transparency.

11. PROMPT: "Now that you have figured out how to use the formula. Solve the sum that you would have to pay me on the 30th day."

#### Assessments

A worksheet will be given to students for assessment. The worksheet will have one section that contains a few problems that deal with geometric sequence and another section that deals with the sum of the geometric sequence. After the students are done with the worksheet, the teacher could go over the answers in class and answer any questions that the students may have.

#### Extensions

Students should know the definition of a sequence and sum of finite sequence beforehand. It maybe helpful if students learned about geometric sequence after the introduction of arithmetic sequence.