Item: tRecursiveRuleOtherRecursive1b

Stem:

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

7, 8, 10, 13, 17, ...

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

Options:

1. an+1 = an + n

2. an+1 = an + 1

3. an+1 = nan

4. an+1 = an + 4

5. an+1 = an + 7

Key:

• Observable: 1. Score: 1; Evidence Value: 1.
  • Student:The expression you selected is correct. Great job!
  • Teacher:The student answered correctly.
• Observable: 2. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. For an = 7, the expression you selected evaluates as: 7 + 1 = 8. The next term is 8, so the rule works for these particular numbers. But it does not work in general. For example, when an = 8, 8 + 1 = 9. But the next term in the sequence is 10, not 9, 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. Think about the following example: The first term is 7, so when n = 1, an = 7. 1 * 7 = 7. But the next term in the sequence is 8, not 7. 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: 4. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. For an = 13, the expression you selected evaluates as: 13 + 4 = 17. The next term is 17, so the rule works for these particular numbers. But it does not work in general. For example, when an = 8, 8 + 4 = 12. But the next term in the sequence is 10, not 12, 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: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. For an = 7, the expression you selected evaluates as: 7 + 7 = 14. But the next term in the sequence is 8, not 14. 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.

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