Arithmetic and Geometric Sequences

Every 3 days, a young tree grows by a certain height. The sequence of heights after each growth period is as follows: 2 cm, 5 cm, 8 cm, 11 cm, 14 cm. Identify the difference in height (in cm) the tree grows every 3 days.

• 2

• -3

• -2

• 3

Tags

CCSS.HSF.BF.A.2

John is saving money every month. He starts by saving $10 in January, $15 in February, $20 in March, $25 in April, and $30 in May. Find the common difference in his savings pattern.

• 5

• 3

• 12

• 8

Tags

CCSS.HSF.BF.A.2

John is saving money. He starts with $3 and decides to double the amount he saves every month. The sequence of his savings over the first five months is: 3, 6, 12, 24, 48. What is the common ratio of this geometric sequence?

• 3

• 2

• 6

• 24

Tags

CCSS.HSF.BF.A.2

Imagine you're planting trees in a pattern where each row has three times as many trees as the previous one. If the first row has 2 trees, followed by 6, 18, 54, and finally 162 trees in subsequent rows, what is the common ratio of this geometric sequence?

• 5

• 3

• 10

• 20

Tags

CCSS.HSF.BF.A.2

Calculate the 10th term of the arithmetic sequence: 4, 7, 10, 13, 16

• 35

• 28

• 31

• 22

Tags

CCSS.HSF.BF.A.2

Imagine you're saving money and you decide to double the amount you save each day starting with $2 on the first day. How much money will you have saved in total by the end of the fifth day?

• $30

• $50

• $40

• $62

Tags

CCSS.HSF.BF.A.2

Every three hours, the water level in a reservoir drops by 3 meters due to evaporation and usage. If the current water level is 15 meters, identify the sequence of water levels for the next 12 hours: 15, 12, 9, 6, 3

• arithmetic

• geometric

• Neither

• exponential

Tags

CCSS.HSF.BF.A.2

John is saving money every month. He starts by saving $4, but then loses $4 each month due to unexpected expenses. What is the common difference in his monthly savings sequence if it starts at $4, then goes to $0, -$4, -$8, and -$12?

• -4

• 6

• 0

• 2

Tags

CCSS.HSF.BF.A.2

Identify the sequence: 5, 10, 20, 40, 80

• geometric

• arithmetic

• linear

• quadratic

Tags

CCSS.HSF.BF.A.2

Find the common ratio in the geometric sequence: 81, 27, 9, 3, 1

• 1/3

• 5

• 2

• 3

Tags

CCSS.HSF.BF.A.2