Understanding Geometric Sequences

This video tutorial explains the concept of geometric sequences, which are sequences where each term after the first is the product of the previous term and a constant called the common ratio. The video provides examples of geometric sequences, discusses their properties, and explains how to identify them. It also covers the general term formula for geometric sequences and highlights the importance of the common ratio not being zero. The tutorial concludes with a summary of the key points discussed.

What is the common rule that defines a geometric sequence?

• Each term is the square of the previous term.

• Each term is the difference of the previous two terms.

• Each term is a fixed multiple of the previous term.

• Each term is the sum of the previous two terms.

Tags

CCSS.HSF.BF.A.2

What is the term used to describe the fixed number that each term is multiplied by in a geometric sequence?

• Common factor

• Common ratio

• Common divisor

• Common difference

Tags

CCSS.HSF.BF.A.2

Which of the following is NOT a characteristic of a geometric sequence?

• The common ratio cannot be zero.

• The sequence can be represented by a general term formula.

• The ratio between consecutive terms is constant.

• The sequence can include zero as a term.

Tags

CCSS.HSF.BF.A.2

How is the general term of a geometric sequence expressed?

• AN = A1 + (N-1)D

• AN = A1 * Q^(N-1)

• AN = A1 / Q^(N-1)

• AN = A1 * N^Q

Tags

CCSS.HSF.BF.A.2

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the third term?

• 18

• 12

• 9

• 6

Tags

CCSS.HSF.BF.A.2

Which of the following sequences is a geometric sequence?

• 3, 6, 10, 15

• 2, 4, 8, 16

• 1, 4, 9, 16

• 1, 2, 4, 7

Tags

CCSS.HSF.BF.A.2

In the sequence AN = 2^(N+1), what is the common ratio?

• 1

• 2

• 3

• 4

Tags

CCSS.HSF.BF.A.2

What happens if the common ratio of a geometric sequence is zero?

• The sequence becomes a constant sequence.

• The sequence becomes a harmonic sequence.

• The sequence becomes undefined.

• The sequence becomes an arithmetic sequence.

Tags

CCSS.HSF.BF.A.2

Which of the following is a valid general term formula for a geometric sequence?

• AN = A1 * Q^(N-1)

• AN = A1 + Q^(N-1)

• AN = A1 * N^(Q-1)

• AN = A1 / Q^(N-1)

Tags

CCSS.HSF.BF.A.2

What is the key difference between an arithmetic sequence and a geometric sequence?

• Arithmetic sequences have a common ratio, geometric sequences have a common difference.

• Arithmetic sequences are always finite, geometric sequences are always infinite.

• Arithmetic sequences have a common difference, geometric sequences have a common ratio.

• Arithmetic sequences are always increasing, geometric sequences are always decreasing.

Tags

CCSS.HSF.BF.A.2