Understanding Recursive and Explicit Rules in Sequences

What are the two methods discussed for describing a sequence?

• Recursive and implicit rules

• Recursive and explicit rules

• Explicit and implicit rules

• Arithmetic and geometric rules

In a recursive rule, how is the next term in a sequence determined?

• By adding a constant to the first term

• By using the previous term and a common difference

• By dividing the previous term by a constant

• By multiplying the previous term by a constant

What is the common difference in the sequence 2000, 2500, 3000?

• 2000

• 1500

• 500

• 1000

How do you determine the starting value for an explicit rule?

• By backtracking to find the zeroth term

• By finding the first term in the sequence

• By calculating the average of the sequence

• By using the last term in the sequence

What is the explicit rule for the sequence starting with 2000 and increasing by 500?

• f(n) = 2000n + 500

• f(n) = 500n + 1500

• f(n) = 500n + 2000

• f(n) = 1500n + 500

Why is it important to verify the explicit rule with examples?

• To find the common difference

• To make the rule more complex

• To confirm the rule accurately describes the sequence

• To ensure the rule is simple

What is the value of f(4) using the explicit rule f(n) = 500n + 1500?

• 3500

• 4000

• 3000

• 2500

In the new sequence example, what is the common difference?

• -24

• 24

• -12

• 12

What is the explicit rule for the sequence starting with 100 and decreasing by 12?

• f(n) = 12n + 112

• f(n) = -12n + 112

• f(n) = 12n + 100

• f(n) = -12n + 100

How is the recursive rule for the new sequence written?

• f(n) = f(n-1) - 24

• f(n) = f(n-1) + 24

• f(n) = f(n-1) - 12

• f(n) = f(n-1) + 12