Item: tRecursiveRuleOtherRecursive2a

Stem:

Let a1, a2, a3,... an,... be a sequence of positive numbers. The first five terms of the sequence are given below.

8, 11, 17, 26, 38, ...

Select the correct rule for finding the (n+1)th term from the nth term.

Options:

1. an+1 = an + 3

2. an+1 = nan

3. an+1 = an + 3n

4. an+1 = an + 8

5. an+1 = an + 12

Key:

• Observable: 1. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. For an = 8, the expression you selected evaluates as: 8 + 3 = 11. The next term is 11, so the rule works for these particular numbers. But it does not work in general. For example, when an = 11, 11 + 3 = 14. But the next term in the sequence is 17, not 14, so the rule fails in this case. It's a good approach to test your rule by checking it with several pairs of numbers from the sequence.
  • Teacher:Student answered incorrectly.
• Observable: 2. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. Think about the following example: The first term is 8, so when n = 1, an = 8. 1 * 8 = 8. But the next term in the sequence is 11, not 8. So this rule does not apply to the sequence given in the question. It's a good approach to test your rule by checking it with several pairs of numbers from the sequence.
  • Teacher:Student answered incorrectly.
• Observable: 3. Score: 1; Evidence Value: 1.
  • Student:The expression you selected is correct. Great job!
  • Teacher:The student answered correctly.
• Observable: 4. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. For an = 8, the expression you selected evaluates as: 8 + 8 = 16. But the next term in the sequence is 11, not 16. So this rule does not apply to the sequence given in the question. It's a good approach to test your rule by checking it with several pairs of numbers from the sequence.
  • Teacher:Student answered incorrectly.
• Observable: 5. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. For an = 26, the expression you selected evaluates as: 26 + 12 = 38. The next term is 38, so the rule works for these particular numbers. But it does not work in general. For example, when an = 11, 11 + 12 = 23. But the next term in the sequence is 17, not 23, so the rule fails in this case. It's a good approach to test your rule by checking it with several pairs of numbers from the sequence.
  • Teacher:Student answered incorrectly.

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