ALG. 1 - CH. 4 (16-17)

Consider the sequence : 729, 243, 81, 27, 9, 3, 1, ... What is the next number in the pattern?

1 x (1/3) = *1/3*

Write the first 5 terms of the sequence given the following characteristics. *geometric sequence *r=5 *first term is 1

1, 5, 25, 125, 625

Write the first 5 terms of the sequence given the following characteristics. *arithmetic sequence *d=5 *first term is 1

1, 6, 11, 16, 21

Write the first 5 terms of the sequence given the following characteristics. *arithmetic sequence *d=350 *first term is 350

350, 700, 1050, 1400, 1750

Determine if the sequence is arithmetic or geometric. Then, identify the next term in the sequence. 100, 75, 50, 25, ...

*arithmetic* *d=-25* *The next term of the sequence is 0.*

Determine if the sequence is arithmetic or geometric. Then, identify the next term in the sequence. 16, 28, 40, 52, ...

*arithmetic* *d=12* *The next term of the sequence is 64.*

What is the common difference in the sequence? 8.5, 8, 7.5, 7, ...

*d=-0.5*

What is the common difference in the sequence? -52, -39, -26, -13, 0, ...

*d=13*

Determine if the sequence is arithmetic or geometric. Then, identify the next term in the sequence. 0.125, 0.25, 0.5, 1, ...

*geometric* *r=2* *The next term of the sequence is 2.*

Determine if the sequence is arithmetic or geometric. Then, identify the next term in the sequence. 1, 4, 16, 64, ...

*geometric* *r=4* *The next term of the sequence is 256.*

What is the common ratio in the sequence? 12, -6, 3, -1.5, ...

*r=-1/2*

What is the common ratio in the sequence? 35, 70, 140, 280, ...

*r=2*

Write the first 5 terms of the sequence given the following characteristics. *arithmetic sequence *d=5 *first term is -15

-15, -10, -5, 0, 5

Write the first 5 terms of the sequence given the following characteristics. *arithmetic sequence *d=13 *first term is -52

-52, -39, -26, -13, 0

Write the first 5 terms of the sequence given the following characteristics. *geometric sequence *r=1/10 *first term is 1000

1000, 100, 10, 1, 1/10

Write the first 5 terms of the sequence given the following characteristics. *geometric sequence *r=-3 *first term is 2

2, -6, 18, -54, 162

Billy is filling his kitchen sink to wash dishes. After one minute there are 2 gallons of water in the sink. After two minutes there are 4 gallons of water in the sink. After 3 minutes there are 6 gallons of water in the sink. *Write a numeric sequence to represent the amount of water in the sink after the first 5 minutes.* *Is this an arithmetic or geometric sequence? How do you know?*

2, 4, 6, 8, 10 This is an arithmetic sequence. I know this because the sink fills up with water at a constant rate and the difference between each consecutive term is the same.

Dave's Pizza made 20 pizzas on Monday, 25 pizzas on Tuesday, and 30 pizzas on Wednesday. If this pattern continues, how many pizzas will Dave's Pizza make on Saturday?

20, 25, 30, 35, 40, 45 Dave's Pizza will make *45* pizzas on Saturday.

Write the first 5 terms of the sequence given the following characteristics. *arithmetic sequence *d=10.5 *first term is 20

20, 30.5, 41, 51.5, 62

Write the first 5 terms of the sequence given the following characteristics. *arithmetic sequence *d=-7 *first term is 212

212, 205, 198, 191, 184

Wayne's Diner is famous for their Philly Cheese-steak Sandwiches. On Monday, Wayne makes 22 Philly Cheese-steak Sandwiches. On Tuesday, Wayne makes 28. On Wednesday, Wayne makes 34. If this pattern continues, how many Philly Cheese-steak Sandwiches will Wayne make on Friday?

22, 28, 34, 40, 46 Wayne will make *46* Philly Cheese-steak sandwiches on Friday.

Write the first 5 terms of the sequence given the following characteristics. *geometric sequence *r=0.05 *first term is 25

25, 1.25, 0.0625, 0.003125, 0.00015625

Consider the sequence : 4, 8, 16, 32, 64, 128, 256, ... What is the next number in the pattern?

256 x 2 = *512*

Write the first 5 terms of the sequence given the following characteristics. *geometric sequence *r=-3 *first term is 3

3, -9, 27, -81, 243

Consider the sequence : 3, 12, 48, 192, 768, 3072, ... What is the next number in the pattern?

3072 x 4 = *12,288*

Write the first 5 terms of the sequence given the following characteristics. *geometric sequence *r=1/4 *first term is 4

4, 1, 1/4, 1/16, 1/64

Write the first 5 terms of the sequence given the following characteristics. *geometric sequence *r=3 *first term is 4

4, 12, 36, 108, 324

Shelby's printer had 400 sheets of paper in it. After Monday, there were 356 sheets of paper. After Tuesday, there were 312 sheets of paper. After Wednesday, there were 268 sheets of paper. If this pattern continues, how many sheets of paper will be left after Friday?

400, 356 (m), 312 (t), 268 (w), 224 (th), *180* (f)

Write the first 5 terms of the sequence given the following characteristics. *arithmetic sequence *d=-1 *first term is 6

6, 5, 4, 3, 2

Describe the pattern and write a numeric sequence to represent the pattern.

Each figure has 1 more dot added to each branch of the x. Each figure has 4 more dots than the previous figure. 5, 9, 13, ...

Describe the pattern and write a numeric sequence to represent the pattern.

Each figure has 1 more row and 1 more column of dots than the previous figure. 1, 4, 9, ...

Describe the pattern and write a numeric sequence to represent the pattern.

Each figure has 1 more row of dots at the bottom. That row has one more dot than the bottom row in the previous figure. 3, 6, 10, ...

Describe the pattern.

Each figure has one less dot on each branch of the cross. This means that each figure has 4 fewer dots than the previous figure.

5, 3, 1, -1, -3, ... Is this sequence arithmetic or geometric? What is the common difference or the common ratio?

This sequence is *arithmetic* and *d=-2*.

1, 4, 16, 64, 256, ... Is this sequence arithmetic or geometric? What is the common difference or the common ratio?

This sequence is *geometric* and *r=4*.

Consider the sequence : 729, 243, 81, 27, 9, 3, 1, ... Describe the pattern.

multiply by 1/3

Consider the sequence : 4, 8, 16, 32, 64, 128, 256, ... Describe the pattern.

multiply by 2

Consider the sequence : 3, 12, 48, 192, 768, 3072, ... Describe the pattern.

multiply by 4