## Arithmetic Sequence

### Xiuqing LiEscambia County Schools

#### Description

Students will examine the concept of arithmetic sequence and learn to find the sum of arithmetic sequence.

#### Objectives

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

#### Materials

- Transparency
- Copies of the worksheet

#### Preparations

1. Teacher should prepare a transparency with definition and examples.
2. Copies of the worksheets, one worksheet per student.

#### Procedures

Note: This lesson only covers arithmetic sequence and series.

1. PROMPT: “A long time ago, there was a student in a math class. Now, his classmates were being very noisy and disruptive, so the math teacher got very, very angry. To punish his students, the teacher told them to add all the integers from 1 until 100. No student could leave the class until he or she was finished with the problem. So everyone began to add the numbers, 1 + 2 = 3. 3 + 3 = 6. 6 + 4 = 10, and so on and so forth. However, this one math student just sat there and thought for a long time. He didn’t write anything down, but after a while, he wrote down the answer and showed it to his teacher. Then, his teacher was amazed that the answer was correct, and the student got home early. So, how did this student figure out how to solve this problem?” It’s anticipated that most students are puzzled.

2. Introduction of topic "arithmetic sequence.”

3. Give the definition of an arithmetic sequence. A sequence is said to be arithmetic if each term, after the first, is obtained from the preceding term by adding a common value. (See attached file)

4. Give examples of arithmetic sequences on the overhead.(see attached file)

5. Find the general term of an arithmetic sequence-the nth term of an arithmetic sequence is an = a1 + (n – 1) d, where a1 is the first term and d is the common difference. (see attached file).

6. Give examples of finding the general term of arithmetic sequence.(see attached file)

7. PROMPT: “Now that you have recognized the pattern of an arithmetic sequence. We can figure out the sum to the problem above. First we have to know the formula for figuring out the sum of an arithmetic sequence.”

8. Definition of the sum of an arithmetic sequence: Sn = n/2 [2a1 + (n - 1) d]. (see attached file).

9. Give examples to find the sum of an arithmetic sequence.(see attached file)

10. PROMPT: “Now that you have practiced how to find the sum of an arithmetic sequence, let’s find the solution to the problem that we had posted.”

#### Assessments

Students will be assessed through the completion of a worksheet in the attached file. After students have completed the worksheet, the teacher can review the answers with the students. Then, similar homework problems can be assigned to help reinforce the concepts learned in the classroom.