Exploring Recursive and Explicit Rules in Arithmetic Sequences

What is the common difference in the sequence 2, 5, 8, 11?

• 3

• 2

• 8

• 5

In the sequence 10, 5, 0, -5, what is the common difference?

• -5

• 5

• 0

• -10

What does 'a sub n' represent in a recursive rule?

• The previous term

• The current term

• The common difference

• The first term

How do you denote the term before 'a sub n' in a recursive rule?

• a sub n + 1

• a sub n

• a sub n - 1

• a sub 1

What is the recursive rule for the sequence 2, 5, 8, 11?

• a sub n = a sub n - 1 - 2

• a sub n = a sub n - 1 - 3

• a sub n = a sub n - 1 + 3

• a sub n = a sub n - 1 + 2

What does 'a sub 1' represent in an explicit rule?

• The previous term

• The current term

• The common difference

• The first term

What is the explicit rule for the sequence 2, 5, 8, 11?

• a sub n = 8 + 3(n - 1)

• a sub n = 5 + 3(n - 1)

• a sub n = 2 + 3(n - 1)

• a sub n = 2 + 5(n - 1)

How can you simplify the explicit rule a sub n = 2 + 3(n - 1)?

• a sub n = 3n - 1

• a sub n = -1 + 3n

• a sub n = 2 + 3n - 3

• a sub n = 2 + 3n

What is the simplified form of the explicit rule a sub n = 8 - 5(n - 1)?

• a sub n = 8 - 5n + 5

• a sub n = 8 - 5n

• a sub n = 13 - 5n

• a sub n = 13 + 5n

Why might you prefer using an explicit rule over a recursive rule?

• It is easier to find the first term

• It is easier to find the previous term

• It is easier to find any term in the sequence

• It is easier to find the common difference