Exploring Arithmetic Sequences

The video tutorial introduces arithmetic sequences, explaining that they are sequences formed by adding a fixed number to each term. It provides examples to illustrate how to identify arithmetic sequences and calculate the common difference. The tutorial also covers how to write rules for these sequences using variable expressions. Advanced examples, including those with decimal numbers, are discussed to reinforce understanding.

What is an arithmetic sequence?

• A sequence where each term is divided by a fixed number

• A sequence where each term decreases by a fixed number

• A sequence where each term is multiplied by a fixed number

• A sequence where each term increases by a fixed number

In the sequence 2, 5, 10, 13, 18, what is the pattern of addition?

• Adding 2, 4, 2, 4

• Adding 5, 3, 5, 3

• Adding 3, 5, 3, 5

• Adding 4, 2, 4, 2

Is the sequence 2, 5, 10, 13, 18 an arithmetic sequence?

• Yes, because it adds numbers

• No, because the numbers added are not fixed

• Yes, because it has a pattern

• No, because it subtracts numbers

What is the common difference in the sequence 2, 4, 6, 8, 10?

• 8

• 6

• 4

• 2

In the sequence 3, -2, -7, -12, what is the common difference?

• 2

• -2

• 5

• -5

How do you write the rule for an arithmetic sequence where each term adds 2?

• n + 2

• n / 2

• n * 2

• n - 2

What does the variable 'n' represent in the rules of arithmetic sequences?

• The last number in the sequence

• The total number of terms

• The first number in the sequence

• Any number in the sequence

What is the common difference in the sequence 21.7, 22.5, 23.3, 24.1?

• 1.2

• 1.0

• 0.8

• 0.5

What is the next term in the sequence 25.7, 26.5 using the identified common difference?

• 27.0

• 27.3

• 26.8

• 27.1

How do you describe the rule for a sequence where each term adds 0.8?

• n + 0.8

• n - 0.8

• n * 0.8

• n / 0.8