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Identify arithmetic and geometric sequences

Todd is reviewing his cell phone bill. When he gets to the text message part, he notices that he sent

100

text messages in November,

83

text messages in December,

66

text messages in January, and

49

text messages in February. What kind of sequence is this?

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Last year, Newport Hardware ordered

32

hammers in December,

96

hammers in January,

288

hammers in February, and

864

hammers in March. What kind of sequence is this?

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While organizing the magazines at the doctor's office, Bob put

5

magazines in the first pile,

8

magazines in the second pile,

13

magazines in the third pile, and

21

magazines in the fourth pile. What kind of sequence is this?

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Farmer Campbell has a plot of tomato plants. There are

3

tomato plants in the first row,

12

tomato plants in the second row,

48

tomato plants in the third row, and

192

tomato plants in the fourth row. What kind of sequence is this?

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What kind of sequence is this?

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1, 4, 9, 16, \dots

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What kind of sequence is this?

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2, 12, 72, 432, \dots

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What kind of sequence is this?

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1, 4, 16, 64, \dots

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What kind of sequence is this?

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2, 8, 32, 128, \dots

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What kind of sequence is this?

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5, 20, 80, 320, \dots

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What kind of sequence is this?

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395, 395, 395, 395, \ldots

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3

students are sharing

2

bags of apple chips. Another group of

6

students are sharing

4

bags of apple chips. The bags are the same size.

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Which group would you rather be in? Explain.

Addison is writing a poem. She writes

5

words on the first line,

10

words on the second line,

20

words on the third line, and

40

words on the fourth line. What kind of sequence is this?

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Sweet Time Bakery just opened and is increasing the number of items they bake. For example, the bakery made

7

carrot cakes in December,

20

carrot cakes in January,

33

carrot cakes in February, and

46

carrot cakes in March. What kind of sequence is this?

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What kind of sequence is this?

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64, 81, 100, 121, \dots

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What kind of sequence is this?

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216, 201, 186, 171, \dots

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What kind of sequence is this?

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81, 100, 121, 144, \dots

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Ayana went out to her garden and cut

16

roses from the first rose bush,

25

roses from the second rose bush,

36

roses from the third rose bush, and

49

roses from the fourth rose bush. What kind of sequence is this?

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While organizing her DVD collection, Savannah put

2

DVDs on the first rack,

14

DVDs on the second rack,

98

DVDs on the third rack, and

686

DVDs on the fourth rack. What kind of sequence is this?

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What kind of sequence is this?

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95, 106, 117, 128, \dots

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While organizing her DVD collection, Janet put

21

DVDs on the first rack,

29

DVDs on the second rack,

37

DVDs on the third rack, and

45

DVDs on the fourth rack. What kind of sequence is this?

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Aisha is drawing stars in her notebook. She draws

103

stars on the first page,

116

stars on the second page,

129

stars on the third page, and

142

stars on the fourth page. What kind of sequence is this?

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Manuel bagged the plastic bottles after a recycling drive. He placed

121

bottles in the first bag,

144

bottles in the second bag,

169

bottles in the third bag, and

196

bottles in the fourth bag. What kind of sequence is this?

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While organizing her DVD collection, Erin put

35

DVDs on the first rack,

50

DVDs on the second rack,

65

DVDs on the third rack, and

80

DVDs on the fourth rack. What kind of sequence is this?

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Meg is writing a poem. She writes

1

word on the first line,

2

words on the second line,

4

words on the third line, and

8

words on the fourth line. What kind of sequence is this?

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Trisha is picking berries in the berry patch. She picks

7

berries from the first bush,

28

berries from the second bush,

112

berries from the third bush, and

448

berries from the fourth bush. What kind of sequence is this?

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What kind of sequence is this?

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1, 5, 25, 125, \dots

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\newline

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While organizing the magazines at the doctor's office, Ava put

67

magazines in the first pile,

47

magazines in the second pile,

27

magazines in the third pile, and

7

magazines in the fourth pile. What kind of sequence is this?

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Frank bagged the plastic bottles after a recycling drive. He placed

149

bottles in the first bag,

165

bottles in the second bag,

181

bottles in the third bag, and

197

bottles in the fourth bag. What kind of sequence is this?

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At a birthday party, the first child receives

735

smiley stickers, the second child receives

735

smiley stickers, the third child receives

735

smiley stickers, and the fourth child receives

735

smiley stickers. What kind of sequence is this?

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What kind of sequence is this?

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1, 8, 64, 512, \dots

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\newline

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Harper is drawing stars in her notebook. She draws

20

stars on the first page,

40

stars on the second page,

120

stars on the third page, and

480

stars on the fourth page. What kind of sequence is this?

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What kind of sequence is this?

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5, 20, 100, 600, \dots

\newline

\newline

\newline

\newline

\newline

What kind of sequence is this?

\newline

4, 20, 100, 500, \ldots

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\newline

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At a birthday party, the first child receives

658

smiley stickers, the second child receives

658

smiley stickers, the third child receives

658

smiley stickers, and the fourth child receives

658

smiley stickers. What kind of sequence is this?

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Emma has a garden and likes to put flowers from her garden into pretty vases. Emma put

3

flowers in the first vase,

9

flowers in the second vase,

27

flowers in the third vase, and

81

flowers in the fourth vase. What kind of sequence is this?

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Last year, Winchester Hardware ordered

6

hammers in September,

30

hammers in October,

150

hammers in November, and

750

hammers in December. What kind of sequence is this?

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While organizing the magazines at the doctor's office, Percy put

4

magazines in the first pile,

9

magazines in the second pile,

16

magazines in the third pile, and

25

magazines in the fourth pile. What kind of sequence is this?

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Trisha's Pizzeria made

9

pizzas on Monday,

16

pizzas on Tuesday,

25

pizzas on Wednesday, and

36

pizzas on Thursday. What kind of sequence is this?

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What kind of sequence is this?

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1, 10, 100, 1,000, \dots

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Megan is picking berries in the berry patch. She picks

53

berries from the first bush,

48

berries from the second bush,

43

berries from the third bush, and

38

berries from the fourth bush. What kind of sequence is this?

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Solve the system by substitution.

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\begin{array}{l} y=4 x \\ y=7 x-30 \end{array}

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(\square, \square)