12_07 Geometric Sequences

Geometric
Sequences

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??

​

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​

Fill in the Blanks

A sequence that has a common difference

Fill in the Blanks

A sequence that has a common ratio

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

• uses multiplication / division​

• common ratio

• exponential functions​

Geometric

• uses addition/subtraction​

• common difference​

• linear functions​

Arithmetic

Arithmetic vs Geometric Sequences

Make sure you know the key differences

Multiple Choice

What is an arithmetic sequence?

A sequence made by ______ the ____ value each time.

• adding; first

• multiplying; same

• adding; same

• multiplying; first

Open Ended

Write the next three terms in this sequence.

{1, 4, 7, ...}

Multiple Choice

Arithmetic sequences change by ADDING the SAME value each time.

Which of these sequences are arithmetic sequences?

a) {3, 6, 12, 24, ...}

b) {32, 16, 8, 4, ...}

• Only a

• Only b

• Both a & b

• Neither

Multiple Choice

Is the sequence 2, 4, 12, 48,... geometric?

• yes
• no

Multiple Choice

Determine whether the sequence is arithmetic, geometric, or neither.

• arithmetic

• geometric

• neither

Multiple Choice

Find the common ratio for the geometric sequence.

• 10
• 1/2
• 2
• 4

Multiple Choice

This image shows how a certain bacteria grows in a petri dish. What is the common ratio of this sequence?

• 4

• 3

• 2

• 6

Open Ended

Find r, the common ratio.

{3, 9, 27, 81, ...}

Multiple Choice

What are the next 3 terms in the following geometric sequence:

512, 256, 128, ___, ___, ___, ...

• 1024, 2048, 4096

• 32, 8, 2

• 64, 32, 16

• 92, 66, 38

Multiple Choice

Find the first four terms of the sequence given the rule:

a_n = 4(5)^n-1

• 20, 100, 500, 2500

• 5, 20, 80, 320

• 4, 20, 100, 500

• 4, 9, 14, 19

Multiple Choice

What is the 14th term of the geometric sequence?

• 14,348,907
• 4,782,969
• 1,594,323
• 45

Multiple Choice

Daisy received $2 on her first birthday. Each year, the amount of money she received tripled. How much money will she receive on her 5^th birthday?

• $10

• $300

• $162

• $416