Item: tTableExtendGeometric2b

Stimulus:

Term Number	Term Value
1
2
3	A
4	B

Stem:

The numbers in the table represent terms in a geometric sequence. Complete the table by filling in the values for A and B.

Inputs:

1. Enter the value for A:
2. Enter the value for B:

Key:

• Observable: 1/45, 1/135. Score: 1; Evidence Value: 1.
  • Student:Right!
  • Teacher:The student correctly generated the next two terms in a geometric sequence with fraction terms, when the sequence was presented in tabular format.
• Observable: 5, 6. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. You may have misread the question.
  • Teacher:The student did not correctly generate the next two terms in a geometric sequence, when the sequence was presented in tabular format. It is possible the student confused term number with term value.
• Observable: -1/15, -1/5. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. The first two terms in the sequence are from a geometric sequence, not from an arithmetic sequence.
  • Teacher:The student did not correctly generate the next two terms in a geometric sequence with fraction terms, when the sequence was presented in tabular format. It is possible the student confused the definition for a geometric sequence with the definition for an arithmetic sequence.
• Observable: 1/75, 1/1125. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. You may have been multiplying adjacent terms, instead of multiplying each term by the common ratio, 1/3.
  • Teacher:The student did not correctly generate the next two terms in a geometric sequence with fraction terms, when the sequence was presented in tabular format. The student may have multiplied adjacent terms.
• Observable: 4/15, 1/3. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. You may have been adding adjacent terms, instead of multiplying each term by the common ratio, 1/3.
  • Teacher:The student did not correctly generate the next two terms in a geometric sequence with fraction terms, when the sequence was presented in tabular format. The student may have added adjacent terms.
• Observable: . Score: 0; Evidence Value: 0.
  • Student:Sorry, that was incorrect.
  • Teacher:Sorry, that was incorrect. In the table, we are given the first two terms of the sequence, 1/5 and 1/15. This information alone is not enough to fill out the table, but we are also told that the terms are from a geometric sequence. This means that the common ratio must be equal to the second term divided by the first term. 1/15 divided by 1/5 is equal to 1/15 times 5, which is 5/15 or 1/3. So the common ratio of this sequence is 1/3. To get the third term, multiply the second term by the common ratio. This is 1/15 times 1/3, or 1/45. To get the fourth term, multiply the third term by the common ratio. This is 1/45 times 1/3, or 1/135. The empty cells in the table should be replaced with the values for the third and fourth terms, so A should be replaced with 1/45 and B should be replaced with 1/135.

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