Item: tRecursiveRuleArithmetic3a

Stem:

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

1.38, 1.42, 1.46, 1.50, ...

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

Options:

1. an+1 = 0.04an + 1.38

2. an+1 = an + 0.04

3. an+1 = 0.04an

4. an+1 = an + 1.38

5. an+1 = an - 0.04

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. You needed to add 0.04 (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: 3. Score: 0; Evidence Value: 0.
  • Student:Sorry, that was incorrect. Instead of multiplying the nth term by 0.04, you needed to add 0.04 to it. 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 1.38 to the nth term, you needed to add 0.04 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 0.04 instead of subtracting 0.04 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.

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