Supplement Lesson for Math 10 Q1 Weeks 1-2

Supplement Lesson for Math 10 Q1 Weeks 1-3

by Sir Aldrin

NOTE:

​

​WE WILL HAVE A POST TEST AFTER THIS LESSON SO BE SURE YOU HAVE UNDERSTOOD ALL BEFORE WE END THIS SESSION.

​

​YOU CAN GO BACK TO THIS LINK ANYTIME FOR A REVIEW. POST TEST WILL HAVE A DEADLINE FOR A FEW DAYS.

​WHAT WE NEED TO LEARN & UNDERSTAND TODAY:

​PART I. SEQUENCE

​1. What is a sequence?

​2. What are the elements of a sequence?

​3. What are the characteristics of a sequence?

​4. What are the types of sequences?

​5. What are the examples for each type of sequence.

What's your

next line?

Open Ended

Please write your answer here.

For you, what did Jolina say in the last part?

​Don't you know that what you did was

​putting something in order.

​By filling up what Jolina said, you were reading and

studying the previous conversations in order to fill up your

own version of appropriate response.

​

​This skill that you have shown is relevant and a necessity

​to our lesson involving SEQUENCE.

​1. So, what is a Sequence?

​Sequences involve patterns. 

​Identify the pattern is a key to recognizing the

​rule of order in sequences.

​

​If you are good at analyzing things,

​our lesson will be "SISIW" for you.

​

​

​We can also illustrate sequences thru pictures.

​For example, can you identify a pattern describe by the figures below?

​Let me know...

Here are my observations.

​Are they same as yours?

​

​What do you think is the next drawing for each sequence?

​2. What are the elements of a sequence?

​Question: Is there a last term?

​​3. What are the characteristics of a sequence?

​Can you classify each sequence below?

A FINITE sequence is definite and has a last term; but

​An INFINITE sequence goes on forever so there is no last term.

Other characteristics of a sequence.​

​4.What are the types of sequence?

​Common

difference?

​Common

​ratio!

​If you noticed, the denominators of a harmonic sequence consists of terms of an arithmetic sequence... 

​   6, 10, 14, 18, 22, 26, 30, 34, 38

​Harmonic sequence in nature

​The height of these sprouting

​plants demonstrate harmonic

sequence:

​Harmonic sequence are also demonstrated in music through the notes. The dots in the arm of a guitar is actually an harmonic division. That is why it is called "harmonic".

​There are many other types of sequence but we will have to concentrate on the 4 examples you have been shown. They are:

​

ARITHMETIC SEQUENCE

​GEOMETRIC SEQUENCE

FIBONACCI SEQUENCE and​

​HARMONIC SEQUENCE

​

Open Ended

Which sequence is easiest for you to identify?

Why? Please give a short explanation.

SHORT QUIZ​

Take note that you will be given a time limit to answer.​

​Ready? Let's go!

Fill in the Blank

1. What follows next in this sequence?

3, 13, 23, 33, 43, _ ?

Fill in the Blank

2. What number comes next in this sequence?

5, 10, 20, 40, 80, _ ?

Multiple Choice

3. Which type of sequence is illustrated in the following example?

1/3, 1/5, 1/7, 1/9, 1/11

• Arithmetic

• Geometric

• Fibonacci

• Harmonic

Multiple Choice

4. Which of the following illustrates a FINITE sequence?

• 1, 0, 1, 0, 1, 0, ...

• 2, 5, 8, 11, 14

• 5, 10, 15, 20, ...

• 1, 2, 3, 4, 5, ...

Multiple Choice

5. Which type of sequence can be found demonstrated in nature thru the number of petals of specific flowers?

• Arithmetic

• Geometric

• Fibonacci

• Harmonic

Multiple Choice

6.Music demonstrates the qualities of which type of sequence?

• Arithmetic

• Geometric

• Fibonacci

• Harmonic

Multiple Choice

7. In an Arithmetic sequence 2, 6, 10, 14, ... the rule is actually...

• subtract 4

• add 4

• multiply by 4

• divide by 4

Multiple Choice

8.What is the common ratio for the Geometric sequence 3, 9, 27, 81, 243, ... ?

• 2

• 3

• 4

• 6

Multiple Choice

9. What is the common difference for the

Arithmetic sequence 10, 8, 6, 4, 2, ... ?

• 2

• -2

• 1/2

• - 1/2

Multiple Choice

10. What is the 7th term of a Fibonacci sequence starting in 1?

Clue: 1, 1, 2, 3, 5, ...

• 8

• 12

• 13

• 15

Fill in the Blank

11. What is the missing term in the Arithmetic sequence below?

12, _ , 6, 3, 0

Fill in the Blank

12. What is the missing term in the Geometric sequence below?

2, 10, _ , 250, 1250

Fill in the Blank

13. What is the missing term of the Harmonic sequence below?

1/4, 1/8, 1/12,  _  , 1/20

Fill in the Blank

14. What is the missing term for the Fibonacci sequence below?

5, 6, 11, _ , 29, 46

Multiple Choice

15. Which sequence has a common difference?

• Arithmetic

• Geometric

• Fibonacci

• Harmonic

Multiple Choice

16. Which sequence has a common ratio?

• Arithmetic

• Geometric

• Fibonacci

• Harmonic

​Don't forget to message me for your questions.

​ -Sir Aldrin