Item: tRecursiveRuleArithmetic1b

Stem:

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

4, 12, 20, 28, ...

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

Options:

1. an+1 = an - 8

2. an+1 = an + 4

3. an+1 = 8an + 4

4. an+1 = an + 8

5. an+1 = 8an

Key:

• Observable: 4. Score: 1; Evidence Value: 1.
  • Student:Good job!
  • Teacher:The student got this item correct.
• Observable: 1. Score: 0; Evidence Value: 0.
  • Student:Sorry, that was incorrect. You needed to add 8 instead of subtracting 8 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: 2. Score: 0; Evidence Value: 0.
  • Student:Sorry, that was incorrect. Instead of adding 4 to the nth term, you needed to add 8 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 8 (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.
• Observable: 5. Score: 0; Evidence Value: 0.
  • Student:Sorry, that was incorrect. Instead of multiplying the nth term by 8, you needed to add 8 to it. To check your answer, apply the rule to two consecutive terms.
  • Teacher:The student did not get this item right.

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