Module 9: Lesson 7: Geometric Sequences

Module 9: Lesson 7: Geometric Sequences

By Mr. Carozza

​Geometric Sequences are very important in investing/saving your money

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Let's learn more​

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Two different ways to show the same thing

Some text here about the topic of discussion

​Explicit Formua

​Recursive Formula

Multiple Choice

What would term a₁ be in the sequence:

4, 8, 16, 32, 64, ...

• 16

• 8

• 4

• 32

Multiple Choice

What is the common ratio (r) in the sequence:

4, 8, 16, 32, 64, ...

• 2

• 4

• 6

• 32

Multiple Choice

What is the common ratio (r) in the sequence:

-2, 16, -128, 768, -6144, ...

• 2

• 8

• -8

• 4

Multiple Choice

Using the sequence: 5, 10, 20, 40, 80, 160, ...

If a₄ = 40, what would a_n-1 be?

• 5

• 10

• 20

• 40

Find a₁ ---> the first term

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Understand what a_n-1 means.... it means the previous term​

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​Recursive Formula

Multiple Choice

Given the sequence: 3, 12, 48, 96, 384, ...

What is a₁?

• 3

• 12

• 48

• 96

Multiple Choice

Given the sequence: 3, 12, 48, 96, 384, ...

What is r?

• 3

• 4

• 12

• 96

Multiple Choice

Given the sequence: 3, 12, 48, 96, 384, ...

What is the recursive formula?

• a₁ = 3 

  a_n = (4) a_n-1

• a₁ = 4 

  a_n = (3) a_n-1

• a₁ = 12 

  a_n = (9) a_n-1

• a₁ = 3 

  a_n = (-9) a_n-1

a₁ = first term

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r = common ratio

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n - 1 = previous term​

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n = desired term​

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​Some text here about the topic of discussion.

​Explicit Formula

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Multiple Choice

Given the sequence: 6, 30, 150, 750, 3750, ...

What is a₁?

• 3750

• 5

• 6

• 150

Multiple Choice

Given the sequence: 6, 30, 150, 750, 3750, ...

What is r?

• 3750

• 5

• 6

• 150

Multiple Choice

Given the sequence: 6, 30, 150, 750, 3750, ...

What is the explicit formula?

• a_n = 5*(5)^n-1

• a_n = 30*(6)^n-1

• a_n = 6*(30)^n-1

• a_n = 6*(15)^n-1

Multiple Choice

Given the sequence: 6, 30, 150, 750, 3750, ...

Use the explicit formula from the previous slide to the find the 8th term?

• 30

• 3750

• 475068

• 468750

Example: 120, 60, 30, 15, 7.5, ...

Sequences can also decrease as well. If the common ratio is less than 1, the sequence decays or declines

Some text here about the topic of discussion

Common ratio less than 1​

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64, 32, 16, 8, 4, ...​

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r = 1/2​

Decay

Common ratio greater than 1

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4, 8, 16, 32, 64, ...​

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r = 2​

Growth

The common ratio determines if the sequence is growth vs. decay

Some text here about the topic of discussion

Multiple Choice

Is the following sequence a growth or decay?

7, 49, 343, 2401, 16807, ...

• Growth

• Decay

Multiple Choice

Is the following sequence a growth or decay?

-20, -60, -360, -2160, -12,960, ...

• Growth

• Decay