Exploring Geometric Sequences with Mrs. Preston

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.

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

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.

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

• 3

• 81

• 9

• 27

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

• 36

• 18

• 162

• 6

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

• 3

• 5

• -5

• -3

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

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

• 96

• 48

• -48

• -96

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

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

• 2

• 5

• 0.5

• 0.2