Item: tCommonRatio2b
Stem:
Find the common ratio for the following geometric sequence:
4, -12, 36, -108, 324, . . .
Inputs:
- Enter your answer here:
Key:
- Observable: -3.
Score: 1;
Evidence Value: 1.
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Student:Right!
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Teacher:The student got this item correct.
- Observable: -16.
Score: 1;
Evidence Value: 1.
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Student:Sorry, that's incorrect. Perhaps you calculated the second term minus the first term. But for this geometric sequence, the difference between successive terms is not the same. For example, -12 minus 4 is -16, but 36 minus -12 is 48. The ratio between successive terms is the same, however.
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Teacher:The student probably confused the common ratio of a geometric sequence with the common difference of an arithemetic sequence.
- Observable: 432.
Score: 1;
Evidence Value: 1.
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Student:Sorry, that's incorrect. Perhaps you calculated the fifth term minus the fourth term. But for this geometric sequence, the difference between successive terms is not the same. For example, -12 minus 4 is -16, but 36 minus -12 is 48. The ratio between successive terms is the same, however.
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Teacher:The student probably confused the common ratio of a geometric sequence with the common difference of an arithemetic sequence.
- Observable: .
Score: 0;
Evidence Value: 0.
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Student:Sorry, that was incorrect.
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Teacher:The student got this item incorrect, but it is not clear why.
Metadata:
Item Node: tCommonRatio2b,
Difficulty: 2.
Proficiencies: CommonRatio.