Intimate geometric and recursive

Question

1.)Comparing explicit and recursive rules.

1. a. Write an explicit rule and recursive rule for the sequence of numbers 3, 8, 13, 18, 23,…
2. b. Find the 1,000th term of the sequence.
3. c. Which rule did you use to find the 1,000th term? Why did you choose that rule?
4. d. What is a disadvantage of a recursive rule when compared to an explicit rule?

Answer 1

The sequence 3, 8, 13, ... is arithmetic with common difference 5.

Explicit definition: a_n = a₁ + (n-1)d

a_n = 3 + (n-1)5 = 5n - 2

Recursive definition:

a₁ = 3

a_n = 5 + a_n-1, if n ≥ 2

a₁₀₀₀ = 5(1000) - 2 = 4998