Math 10 Online Aug. 23

Math 10 Online Aug. 23

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?

Open Ended

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

Open Ended

How is each term (number of matchsticks) found?

Open Ended

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:

Fill in the Blanks

Read the directions carefully.

Is the given sequence, arithmetic? If yes, find the common difference then find the next four terms. If it is not an arithmetic sequence, write NOT.

6, 13, 20, 27

Format of your answers should be like this: d=1 1, 2, 3, 4, 5

Fill in the Blanks

Read the directions carefully.

Is the given sequence, arithmetic? If yes, find the common difference then find the next four terms. If it is not an arithmetic sequence, write NOT.

4, -5, -14, -25,

Format of your answers should be like this: d=1 1, 2, 3, 4, 5

Fill in the Blanks

Read the directions carefully.

Is the given sequence, arithmetic? If yes, find the common difference then find the next four terms. If it is not an arithmetic sequence, write NOT.

-3, -3, -3, -3

Format of your answers should be like this: d=1 1, 2, 3, 4, 5

Fill in the Blanks

B. Write the first five terms of sequence with the given nth term. If it is an arithmetic sequence, include the common difference.

$a_n=7+4n$  

Format of your answers should be like this: d=1 1, 2, 3, 4, 5

if there's no common difference, do not write d=

Fill in the Blanks

B. Write the first five terms of sequence with the given nth term. If it is an arithmetic sequence, include the common difference.

$a_n=4\left(1-n\right)+10$  

Format of your answers should be like this: d=1 1, 2, 3, 4, 5

if there's no common difference, do not write d=

Fill in the Blanks

B. Write the first five terms of sequence with the given nth term. If it is an arithmetic sequence, include the common difference.

$a_n=2n+\left(-1\right)^n$  

Format of your answers should be like this: d=1 1, 2, 3, 4, 5

if there's no common difference, do not write d=

Fill in the Blanks

C. Find the 75th term of the given arithmetic sequence:

-18, -7, 4, 15

Fill in the Blanks

C. Find the 40th term of the given arithmetic sequence:

$11,\ \frac{17}{2},\ 6,\ \frac{7}{2}$  

Fill in the Blanks

C. Find the 51st term of the given arithmetic sequence:

$2\sqrt[]{3},\ 5\sqrt[]{3},\ 8\sqrt[]{3},\ 11\sqrt[]{3}$  

If you need to input a special character, copy it from MS word first then paste it on the space for your answer.

Fill in the Blanks

C. Find the 100th term of the given arithmetic sequence:

$2.2,\ 4.5,\ 6.8,\ 8.1$  

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

Open Ended

One/ two thing/s you have learned

Open Ended

One question you still have

Open Ended

One thing you want to know more