Item: tRecursiveRuleOtherRecursive1a

Stem:

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

3, 4, 6, 9, 13, ...

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

Options:

1. an+1 = nan

2. an+1 = an + 4

3. an+1 = an + 3

4. an+1 = an + 1

5. an+1 = an + n

Key:

• Observable: 1. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. Think about the following example: The first term is 3, so when n = 1, an = 3. 1 * 3 = 3. But the next term in the sequence is 4, not 3. 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: 2. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. For an = 9, the expression you selected evaluates as: 9 + 4 = 13. The next term is 13, so the rule works for these particular numbers. But it does not work in general. For example, when an = 4, 4 + 4 = 8. But the next term in the sequence is 6, not 8, 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: 3. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. For an = 6, the expression you selected evaluates as: 6 + 3 = 9. The next term is 9, so the rule works for these particular numbers. But it does not work in general. For example, when an = 4, 4 + 3 = 7. But the next term in the sequence is 6, not 7, 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: 4. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. For an = 3, the expression you selected evaluates as: 3 + 1 = 4. The next term is 4, so the rule works for these particular numbers. But it does not work in general. For example, when an = 4, 4 + 1 = 5. But the next term in the sequence is 6, not 5, 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: 5. Score: 1; Evidence Value: 1.
  • Student:The expression you selected is correct. Great job!
  • Teacher:The student answered correctly.

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