Geometric Sequences and Their Properties

The video tutorial covers geometric sequences, focusing on the explicit formula. It explains how to determine if a sequence is geometric by identifying the common ratio and demonstrates how to find the eighth term using the formula. The tutorial includes examples with different common ratios and provides practice problems for students to apply their learning.

What is the main operation used in geometric sequences to move from one term to the next?

• Addition

• Subtraction

• Multiplication

• Division

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CCSS.HSF.BF.A.2

In a geometric sequence, what does the letter 'r' represent?

• Last term

• Common ratio

• Common difference

• First term

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CCSS.HSF.BF.A.2

How do you determine if a sequence is geometric?

• Check if each term is added by a constant

• Check if each term is multiplied by a constant

• Check if each term is subtracted by a constant

• Check if each term is divided by a constant

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CCSS.HSF.BF.A.2

What is the explicit formula for a geometric sequence?

• a_n = a_1 + (n-1)d

• a_n = a_1 / r^(n-1)

• a_n = a_1 * r^(n-1)

• a_n = a_1 - r^(n-1)

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CCSS.HSF.BF.A.2

If the first term of a geometric sequence is -4 and the common ratio is 2, what is the eighth term?

• -128

• -384

• -512

• -256

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CCSS.HSF.BF.A.2

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

• 4

• 3

• 2

• 5

Tags

CCSS.HSF.BF.A.2

How can you verify the common ratio of a geometric sequence?

• By dividing each term by the previous term

• By subtracting each term from the next term

• By multiplying each term by the next term

• By adding the first and last terms

Tags

CCSS.HSF.BF.A.2

What is the first term of a geometric sequence if the explicit formula is a_n = 3 * 3^(n-1)?

• 9

• 27

• 3

• 1

Tags

CCSS.HSF.BF.A.2

Using the explicit formula a_n = -3 * 2^(n-1), what is the fourth term?

• -6

• -12

• -24

• -48

Tags

CCSS.HSF.BF.A.2

What is the eighth term of the sequence defined by a_n = -3 * 2^(n-1)?

• -256

• -512

• -384

• -192

Tags

CCSS.HSF.BF.A.2