Item: tRecursiveRuleArithmetic2b

Stem:

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

4.84, 11.84, 18.84, 25.84, ...

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

Options:

1. an+1 = 7an

2. an+1 = an + 7

3. an+1 = an - 7

4. an+1 = an + 4.84

5. an+1 = 7an + 4.84

Key:

• Observable: 2. Score: 1; Evidence Value: 1.
  • Student:Right!
  • Teacher:The student got this item correct.
• Observable: 1. Score: 0; Evidence Value: 0.
  • Student:Sorry, that was incorrect. Instead of multiplying the nth term by 7, you needed to add 7 to it. To check your answer, apply the rule to two consecutive terms.
  • Teacher:The student did not get this item right.
• Observable: 3. Score: 0; Evidence Value: 0.
  • Student:Sorry, that was incorrect. You needed to add 7 instead of subtracting 7 from the nth term because it's an increasing sequence. To check your answer, apply the rule to two consecutive terms.
  • Teacher:The student did not get this item right.
• Observable: 4. Score: 0; Evidence Value: 0.
  • Student:Sorry, that was incorrect. Instead of adding 4.84 to the nth term, you needed to add 7 to it. To check your answer, apply the rule to two consecutive terms.
  • Teacher:The student did not get this item right.
• Observable: 5. Score: 0; Evidence Value: 0.
  • Student:Sorry, that was incorrect. You needed to add 7 (the common difference) to the nth term to get the (n+1)th term. To check your answer, apply the rule to two consecutive terms.
  • Teacher:The student did not get this item right.

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