Geometric Sequences

Writing Geometric Sequences

By Jala Hawkins

​F.IF.3: I can identify, write, and create geometric sequences.

• uses multiplication / division​

• common ratio

• exponential functions​

Geometric (Unit 4)

• uses addition/subtraction​

• common difference​

• linear functions​

Arithmetic (Unit 2)

Arithmetic vs Geometric Sequences

Make sure you know the key differences

How to find common ratio?

3, 6 , 12, 24, 48, ...

Ask yourself: What are they multiplying by each time to get to the next number? 3 * _ = 6??

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OR

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Take one number and divide it by the one before it!​ example: 24/12

​Both ways get us a common ratio of

2​

Multiple Choice

What is the common ratio?

• -2

• 2

• 4

• Not enough information

Multiple Choice

What is the common ratio?

• 5

• -5

• 3

• Not enough information

Multiple Choice

Find the common ratio for the geometric sequence.

• 2
• -2
• 1/2
• -1/2

Multiple Choice

What is a₅?

• -1875

• -550

• -1055

• Not enough information

Multiple Choice

What is a₅ ?

• -64

• -24

• -32

• Not enough information

Explicit:

We only need to find a₁ (first term) and r(common ratio)​

How to write formulas for geometric sequences

Some text here about the topic of discussion

Multiple Choice

What is the explicit expression that represents how many strings are included based on the number of steps?

• $$\frac{1}{2}n+2$$  

• $$-n+2$$  

• $$\frac{1}{2}n$$  

• $$4\left(\frac{1}{2}\right)^n$$  

Multiple Choice

Write the explicit formula for the geometric sequence.

• a_n = 10(2)^n-1
• a_n = 2(10)^n-1
• a_n = 10(2)ⁿ
• a_n = 2(10)ⁿ

Multiple Choice

Write the explicit formula for the geometric sequence.

• a_n = 4(3)^n-1
• a_n = 3(4)^n-1
• a_n = -4(3)^n-1
• a_n = 3(-4)^n-1

Multiple Choice

What is a₅ ?

• -64

• -24

• -32

• Not enough information