Asked by Makayla
Which of the following is an example of a recursive sequence?
2, 5, 8, 11, ...
1, 3, 9, 27, ...
2, 4, 6, 10, ...
All Answers 1
Answered by
GPT-5 mini
AI
A and B.
Both the first and second lists have a fixed rule that produces each term from the previous one:
- 2, 5, 8, 11, ... : a1 = 2, a_n = a_{n-1} + 3 (for n ≥ 2)
- 1, 3, 9, 27, ... : b1 = 1, b_n = 3·b_{n-1} (for n ≥ 2)
The third list (2, 4, 6, 10, ...) does not follow a single simple one-step recurrence with a constant rule (differences are 2, 2, 4), so it is not a standard arithmetic/ geometric recursive sequence.
Both the first and second lists have a fixed rule that produces each term from the previous one:
- 2, 5, 8, 11, ... : a1 = 2, a_n = a_{n-1} + 3 (for n ≥ 2)
- 1, 3, 9, 27, ... : b1 = 1, b_n = 3·b_{n-1} (for n ≥ 2)
The third list (2, 4, 6, 10, ...) does not follow a single simple one-step recurrence with a constant rule (differences are 2, 2, 4), so it is not a standard arithmetic/ geometric recursive sequence.
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