Understanding Arithmetic Sequences

The video tutorial explains how to determine if a sequence is arithmetic by checking if a constant is added to each term to get the next. It provides examples of both arithmetic and non-arithmetic sequences, demonstrating how to calculate the common difference using a formula. The tutorial emphasizes that if different values for the common difference are found, the sequence is not arithmetic. It concludes with examples of sequences with common differences of 5 and 3.

What defines an arithmetic sequence?

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

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

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

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

Tags

CCSS.HSF.BF.A.2

In the first sequence, what is the common difference?

• 6

• 3

• 4

• 5

Tags

CCSS.HSF.BF.A.2

How can you confirm a sequence is arithmetic using terms?

• By checking if the product of consecutive terms is constant.

• By checking if the sum of consecutive terms is constant.

• By checking if the ratio between consecutive terms is constant.

• By checking if the difference between consecutive terms is constant.

Tags

CCSS.HSF.BF.A.2

Why is the second sequence not arithmetic?

• The common difference is not consistent.

• The terms are not in increasing order.

• The terms are not in decreasing order.

• The sequence has a common ratio instead.

Tags

CCSS.HSF.BF.A.2

What is the common difference between the first two terms of the second sequence?

• -7

• -6

• -5

• -4

Tags

CCSS.HSF.BF.A.2

In the third sequence, what is the difference between the second and first term?

• 4

• 10

• 5

• 6

Tags

CCSS.HSF.BF.A.2

Why is the third sequence not considered arithmetic?

• The sequence has a constant ratio.

• The sequence has a constant sum.

• The sequence has varying differences.

• The sequence has a constant product.

Tags

CCSS.HSF.BF.A.2

What is the common difference in the fourth sequence?

• 5

• 2

• 3

• 4

Tags

CCSS.HSF.BF.A.2

How can you verify the common difference in the fourth sequence?

• By subtracting the first term from the last term.

• By adding the first term to the last term.

• By dividing consecutive terms and checking for consistency.

• By subtracting consecutive terms and checking for consistency.

Tags

CCSS.HSF.BF.A.2

What is the result of subtracting the third term from the fourth term in the fourth sequence?

• 5

• 4

• 3

• 2

Tags

CCSS.HSF.BF.A.2