Item: tCommonRatio3a

Stem:

Find the common ratio for the following geometric sequence:

0.32, 0.16, 0.08, 0.04, 0.02, . . .

Inputs:

1. Enter your answer here:

Key:

• Observable: 0.5. Score: 1; Evidence Value: 1.
  • Student:Right!
  • Teacher:The student got this item correct.
• Observable: -0.16. Score: 1; Evidence Value: 1.
  • 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, 0.16 minus 0.32 is -0.16, but 0.08 minus 0.16 is -0.08. The ratio between successive terms is the same, however.
  • Teacher:The student probably confused the common ratio of a geometric sequence with the common difference of an arithemetic sequence.
• Observable: -0.02. Score: 1; Evidence Value: 1.
  • 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, 0.16 minus 0.32 is -0.16, but 0.08 minus 0.16 is -0.08. The ratio between successive terms is the same, however.
  • 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.
  • Student:Sorry, that was incorrect.
  • Teacher:The student got this item incorrect, but it is not clear why.

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