Geometric Sequence

Intermediate Algebra

April 4, 2023

Observe the set of numbers in the given figures. Determine what value is used to replace the question mark in the given puzzle.

​Activity 1. SOLVE ME!

Observe the set of numbers in the given figures. Determine what value is used to replace the question mark in the given puzzle.

​Activity 1. SOLVE ME!

​10

Observe the set of numbers in the figure. Determine what value is used to replace the question mark in the given puzzle.

​Activity 1. SOLVE ME!

Observe the figure. Determine what pattern is used in the given set of numbers to solve the puzzle?

​What will replace ?

​What's the Pattern?

​10

​What type of Sequence could be associated with this?

​10

​What type of Sequence could be associated with this?

Activity 2. Complete Me!

​Complete the table by identifying the correct term. Select your answer from the given choices.

Activity 2. Complete Me!

T) -3 3 13 C) 6 21 46 I) -4 -32 -1034

A) 8 20 40 O) 6 48 1536 ​ R) 6 15 30

Open Ended

What word is formed?

Open Ended

Tell something about the Ratio. What do you know about it? How is it being used in Mathematics?

• compares two numbers in order

• relationship or comparison between two numbers

  • a/b

​Ratio

Find the ratio of the second number (b) to the first number (a). Select your answer from the given choices.

Activity 3. Divide Me

Multiple Choice

DIVIDE ME!

a) 2, b) 16

• A. $$\frac{16}{2}$$

• B. $$8$$

• C. $$\frac{2}{16}$$

• D. $$\frac{1}{8}$$

Multiple Choice

DIVIDE ME!

a) 18 b) -6

• A. $$\frac{18}{-6}$$

• B. $$-3$$

• C. $$\frac{-6}{18}$$

• D. $$\frac{-1}{3}$$

Multiple Choice

DIVIDE ME!

a) 2m b) 4m

• A. $$\frac{2m}{4m}$$

• B. $$\frac{1}{2}$$

• C. $$2$$

• D. $$\frac{4m}{2m}$$

Multiple Choice

DIVIDE ME!

a) ab b) $$a^2b^2$$

• A. $$\frac{ab}{a^2b^2}$$

• B. $$\frac{1}{ab}$$

• C. $$ab$$

• D. $$\frac{a^2b^2}{ab}$$

Multiple Choice

DIVIDE ME!

a) $$\frac{1}{8}$$ b) $$\frac{1}{16}$$

• A. $$\frac{16}{8}$$

• B. $$2$$

• C. $$\frac{8}{16}$$

• D. $$\frac{1}{2}$$

Activity 4. Connect Me!

Directions​

1. Start with one clothes peg or pin.

2. Attach the more pins to the tails of the peg.

3. Continue to attach more pegs until the last peg you have.

Connection	​1	​2	​3	​4
No. of Clips	​	​	​	​

PEACOCK

" a male peafowl, which has very long tail feathers that have eye-like markings and can be erected and fanned out in display. "

Early Christians saw the peacock as a symbol of Christ’s resurrection. Although mentioned only once in the Bible—when King Solomon acquires the wealth of Tarshish: “gold, and silver, ivory, and apes, and peacocks”—the Christian tradition picked up the bird through St. Augustine of Hippo. In “City of God,” Augustine lauds the striking beauty of a peacock in full fan and notes that peacock flesh doesn’t spoil as quickly as meat from other birds. He compares this to Christ’s resurrection through his sacrifice on Calvary. The peacock flaunts a fleeting beauty, Augustine says, but its undying flesh reminds Christians of the immortality that comes from God’s eternal love.

PEACOCK

The ancient Greeks believed that the flesh of the peacock never decayed, even after death, and so it became a symbol of immortality. Early Christians adopted the symbolism and the peacock thus became an emblem of the Resurrection and the eternal life of Christ.

symbol for power, strength, confidence, and even divinity

Connections	​1	​2	​3	​4
Clips	​2	​4	​8	​16

​1, 2, 4, 8, 16

1. How many connections did you have?

2. Is there a pattern in the number of pegs

obtained after 4 connections?

3. You have generated a sequence of pegs.

What are the first 4 terms of the sequence?

4. Is the sequence an arithmetic sequence?

Why?

​

​Questions:

GEOMETRIC SEQUENCE

Geometric Sequence

1.) 64, 32, 16, 8, 4, ...

2.) 7, 21, 63, 189, ...

Geometric Sequence

1.) 64, 32, 16, 8, 4, .. .

2.) 7, 21, 63, 189, ...

Geometric Sequence

a sequence such that the terms, after the first, are formed by multiplying or dividing the preceding term by a non-zero constant called common ratio.

​General Term

​

3.) 1, 3, 9, 27, 81, 243, 729, ...

1.) 64, 32, 16, 8, 4, .. .

2.) 7, 21, 63, 189, ...

​Example:

​

​Example 4:

​

​

​

​

​Activity 5. Next Please...

​Activity 5. Next Please...

​Activity 5. Next Please...

​Activity 5. Next Please...

​Activity 5. Next Please...

​Real Life Applications of Geometric Sequence

​

​Economics

​Interest Rate

​Economics

​Price of commodities

Science/Health

​Bacteria/Viruses

Music

​Octaves

Arts

P. E (Sports)

P. E (Sports)

Languages

​Communication

Multiple Choice

Identify the common ratio.

17, -51, 153, -459, …

• 3

• 1/3

• -3

• -1/3

Multiple Choice

Identify the common ratio.

-4, 24,-144, 864,…

• 1/6

• 6

• -1/6

• -6

Multiple Choice

Identify the common ratio.

2/3, 2, 6, 18,…

• 3

• 3/2

• 2/3

• -3

​ACTIVITY 6. COMPARE AND CONTRAST

​A.) Group yourself according to your line of interest

1. Song composers

2. Poem writers

3. Video editors

4. Illustrators

B.) Present your answer to the question, "What is the difference

between arithmetic sequence and geometric sequence?"

​Criteria/Rubrics	​5-Excellent	​4-Good	​3-Fair
​Delivery	​Shows confidence and mastery in all of the presentation	​​Shows confidence and mastery in some but not all parts of the presentation	​Neither confidence nor mastery has shown.
​Presentation	​Elements that are needed to present are cohesively into each other.	​​Elements that are needed to present is good but it has a bit unclear explanation.	​Elements that are needed to present is good but not well organized
​Content	​Interesting content with fresh perspective.	​It includes essential information about the topic	​It includes basic information needed about the topic
​Creativity/Originality	​The ideas are unique and witty. It shows a great originality.	​Uses ideas from other references/resources (youtube/google) but there is a little evidence of original ideas.	​The ideas are copied from other references/resources (youtube/google) but there is a big evidence of original ideas.