Objectives:

​Students will be able to:

1. Illustrate an arithmetic sequence

2. Identify whether a sequence is arithmetic or not

3. Determine the common difference

4. Determine the nth term of a given arithmetic sequence

​Action

​By group, follow the instructions below and answer the following guide questions.

1.Below are squares formed by matchsticks.

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​2. Count the number of matchsticks in each figure and record the results in a table

​Guide Questions

​1.Is there a pattern in the number of matchsticks? If there is, describe it.

2.How is each term (number of matchsticks) found?

3.What is the difference between any two consecutive terms?

​Analysis

​•Suppose we want to find the 20th, 50th and 100th terms of the sequence. How do we get them?

•Do you think a formula would help?

​Consider the table below and complete it. Observe how each term is rewritten.

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What is a₅? a₂₀? a₅₀?

What is the formula for determining the number of matchsticks needed to form n squares?

​​Arithmetic Sequence

is a sequence where every term after the first is obtained by adding a constant called common difference.

​Common Difference

difference between any two consecutive terms that is constant.

​In general, the first n terms of an arithmetic sequence with a₁ as first term and d as common difference is given by a_n=a₁+(n-1)d

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If a₁ and d are known, it is easy to find any term in an arithmetic sequence.

​Examples:

​1. What is the 10th term of the arithmetic sequence 5, 12, 19, 26, ...?

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​2. What is the 8th term of the arithmetic sequence 3, 12, 21, ...?

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​3. The fourth term of an arithmetic sequence is 27, and the eleventh term is 69. Find the common difference, the first term, and the 25th term of the sequence.

​Solution:

​1. What is the 10th term of the arithmetic sequence 5, 12, 19, 26, ...?

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​Solution:

​2. What is the 8th term of the arithmetic sequence 3, 12, 21, ...?

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​Solution:

​3. The fourth term of an arithmetic sequence is 27, and the eleventh term is 69. Find the common difference, the first term, and the 25th term of the sequence.

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Answer the exercises in your book page 15 letter A (#s 1-3), B (1-3) & C (1-4)​

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​Write your solutions in your notebook, take a picture of it then upload it Gdrive.

​Input your final answers in the next slides for checking.

​Application:

Assignment:

​Write about two stories or more Biblical narratives you have read that shows pattern. Explain how do you think they have shown pattern.

​Write it in your notebook, take a picture of it then upload it to Gdrive