Geometric Sequences and Series

Geometric Sequences

Some text here about the topic of discussion

​Explicit 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

a₁ = first term

​

r = common ratio

​

n - 1 = previous term​

​

n = desired term​

​

​

​Explicit Formula

​

Multiple Choice

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

What is a₁?

• 3

• 12

• 48

• 96

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

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

Common ratio less than 1​

​

64, 32, 16, 8, 4, ...​

​

r = 1/2​

Decay

Common ratio greater than 1

​

4, 8, 16, 32, 64, ...​

​

r = 2​

Growth

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

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

Multiple Choice

Find the next three terms: 4, 12, 36, 108, ...

• 324, 972, 2916

• 972, 2916, 8748

• 405, 1215, 3645

Multiple Choice

Which sequence is represented by the equation 2(7)^n-1 ?

• 7, 14, 28, 56...

• 2, 14, 98, 686...

• 2, 9, 16, 23...

• 7,9,11,13...

Fill in the Blank

What is the sum of the first five terms of the sequence 5,15,45,...? On the problem, what is the first term?

Fill in the Blank

What is the sum of the first five terms of the sequence 5,15,45,...? On the problem, what is the common ratio?

Fill in the Blank

On the problem, how many terms are to be added?

Fill in the Blank

What is the sum of the first five terms of the sequence 5,15,45,...?