Item: tTableExtendGeometric3a

Stimulus:

Stem:

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

Hint: the term numbers are not listed consecutively.

Inputs:

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

Key:

• Observable: 16, 4. Score: 1; Evidence Value: 1.
  • Student:Right!Excellent work.
  • Teacher:The student was able to identify find missing, non-consecutive terms in a geometric sequence.
• Observable: 16, 5. Score: 1; Evidence Value: 1.
  • Student:Your answer for A is correct, but you did not correctly idenfity the value for B.
  • Teacher:The student may have difficulty finding missing, non consecutive terms in a geometric sequence.
• Observable: 4, 4. Score: 1; Evidence Value: 1.
  • Student:Your answer for B is correct, but you did not correctly idenfity the value for A.
  • Teacher:The student may have difficulty finding missing, non consecutive terms in a geometric sequence.
• Observable: 2, 4. Score: 1; Evidence Value: 1.
  • Student:Your answer for B is correct, but you did not correctly idenfity the value for A.
  • Teacher:The student may have difficulty finding missing, non consecutive terms in a geometric sequence.
• Observable: 8, 4. Score: 1; Evidence Value: 1.
  • Student:Your answer for B is correct, but you did not correctly idenfity the value for A.
  • Teacher:The student may have difficulty finding missing, non consecutive terms in a geometric sequence.
• Observable: . Score: 0; Evidence Value: 0.
  • Student:Sorry, that was incorrect. In the table, we are given the value for the first term, 1, and the sixth term, 1024. 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 there is a common ratio between successive terms. Since 1 is the first term and 1024 is the sixth term, we need to multiply by the common ratio 5 times to get from 1 to 1024. What number raised to the 5th power is equal to 1024? The answer is 4, which is the common ratio of this sequence. To get the third term, multiply the first term by the common ratio squared. This is 1 times 16, or 16. The next term given is 64. 64 divided by 16 is 4, which is the common ratio. So 64 must be the term immediately following 16, which means it is the fourth term. One empty cell in the table should be replaced with the value for the third term. So A should be replaced with 16. The other empty cell in the table should be replaced with the term number corresponding to 64. So B should be replaced with 4.
  • Teacher:The student got this item incorrect, but it is not clear why.

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