Mrs. Preston explains geometric and arithmetic sequences, focusing on identifying sequence types, finding common ratios, and writing equations. She provides examples to illustrate how to determine if a sequence is arithmetic or geometric, how to calculate the common ratio, and how to write equations for sequences. The video also covers finding specific terms in a sequence using these equations, with practice problems to reinforce learning.

What is a geometric sequence?

• A sequence where each term is added by a constant value.

• A sequence where each term is multiplied by a constant value.

• A sequence where each term is subtracted by a constant value.

• A sequence where each term is divided by a constant value.

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CCSS.HSF.BF.A.2

In a geometric sequence, what is the term used to describe the constant factor between consecutive terms?

• Common difference

• Common factor

• Common multiplier

• Common ratio

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CCSS.HSF.BF.A.2

How do you determine if a sequence is arithmetic?

• By checking if each term is subtracted by the same amount.

• By checking if each term is divided by the same amount.

• By checking if each term is added by the same amount.

• By checking if each term is multiplied by the same amount.

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CCSS.HSF.BF.A.2

What is the common ratio in the sequence 3, 9, 27, 81?

• 3

• 81

• 9

• 27

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CCSS.HSF.BF.A.2

If a sequence has a common ratio of 1/3, what is the next term after 54?

• 36

• 18

• 162

• 6

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CCSS.HSF.BF.A.2

What is the common ratio in the sequence 3, -15, 75, -375?

• 3

• 5

• -5

• -3

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CCSS.HSF.BF.A.2

How do you write the rule for a geometric sequence with the first term 3 and common ratio 2?

• a(n) = 3 * 2^(n-1)

• a(n) = 3 + 2^n

• a(n) = 3 + 2^(n-1)

• a(n) = 3 * 2^n

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CCSS.HSF.BF.A.2

What is the 5th term in the geometric sequence with the first term -3 and common ratio 2?

• 96

• 48

• -48

• -96

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CCSS.HSF.BF.A.2

What is the 12th term in the geometric sequence with the first term 6 and common ratio 0.4?

• 0.00025

• 0.0025

• 0.025

• 0.25

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CCSS.HSF.BF.A.2

What is the common ratio in the sequence 625, 125, 25, 5?

• 2

• 5

• 0.5

• 0.2

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CCSS.HSF.BF.A.2