Geometric Sequences and Common Ratios

The video tutorial covers geometric sequences, focusing on understanding and finding the common ratio, deriving the nth term formula, and applying these concepts to solve problems. It begins with an introduction to geometric sequences, explaining the concept of a common ratio. The tutorial then demonstrates techniques to find the common ratio, including examples with different types of sequences. It proceeds to derive the formula for the nth term of a geometric sequence and applies this formula to solve various problems, including finding specific terms and determining when a sequence exceeds a certain value.

What is the common ratio in a geometric sequence where each term is multiplied by 2?

• 3

• 0.5

• 2

• 1

Tags

CCSS.HSF.BF.A.2

If a geometric sequence has a common ratio of 2/3, what is the next term after 18?

• 8

• 27

• 12

• 16

Tags

CCSS.HSF.BF.A.2

In an alternating geometric sequence, what is the common ratio if the sequence oscillates between 5 and -5?

• 1

• 0.5

• -0.5

• -1

Tags

CCSS.HSF.BF.A.2

What is the common ratio in the sequence: x, x^2, x^3?

• x

• 1/x

• x^3

• x^2

Tags

CCSS.HSF.BF.A.2

Given the second term of a geometric sequence is 4 and the fourth term is 8, what is the common ratio?

• √2

• 2

• 1/2

• 4

Tags

CCSS.HSF.BF.A.2

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

• √2

• 2

• 4

• 2√2

Tags

CCSS.HSF.BF.A.2

In a geometric sequence, if the second term is 6 and the common ratio is 2, what is the tenth term?

• 3072

• 1536

• 768

• 512

Tags

CCSS.HSF.BF.A.2

What is the common ratio in a geometric sequence where the second term is x and the third term is x+6?

• x/6

• x+3

• x+6/x

• x/3

Tags

CCSS.HSF.BF.A.2

If the common ratio of a geometric sequence is 2 and the first term is 3, what is the first term to exceed 1 million?

• 19th term

• 22nd term

• 20th term

• 21st term

Tags

CCSS.HSF.BF.A.2

Given the third term of a geometric sequence is 20 and the fifth term is 80, what is the common ratio?

• 2

• 4

• √4

• √2

Tags

CCSS.HSF.BF.A.2