Item: tTableExtendGeometric3b
Stimulus:
| Term Number |
Term Value |
| 1 |
2 |
| 2 |
A |
| B |
16 |
| 6 |
64 |
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:
- Enter the value for A:
- Enter the value for B:
Key:
- Observable: 4,
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: 4,
3.
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,
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: 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, 2, and the sixth term, 64. 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 2 is the first term and 64 is the sixth term, we need to multiply by the common ratio 5 times to get from 2 to 64. 64 divided by 2 is 32. What number raised to the 5th power is equal to 32? The answer is 2, which is the common ratio of this sequence. To get the second term, multiply the first term by the common ratio. This is 2 times 2, or 4. The next term given is 16. 16 divided by 4 is 4, which is the common ratio squared. So 16 must be two terms after 4, which means it is the fourth term. One empty cell in the table should be replaced with the value for the second term. So A should be replaced with 4. The other empty cell in the table should be replaced with the term number corresponding to 16. So B should be replaced with 4.
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Teacher:The student got this item incorrect, but it is not clear why.
Metadata:
Item Node: tTableExtendGeometric3b,
Difficulty: 3.
Proficiencies: TableGeometric,
ExtendGeometric.