Item: tExamplesGeometric1b

Stem:

Give the first 3 terms of a geometric sequence that satisfies the following:

1. The first term is a positive integer between 1 and 3, inclusive.

2. The common ratio is a positive integer between 3 and 5, inclusive.

Note: There is more than one correct answer. Any example you choose that meets the above requirements will be scored as correct.

Inputs:

1. Enter your answers here:
2. ,
3. and

Key:

• Observable: 1, 3, 9. Score: 1; Evidence Value: 1.
  • Student:Right! You correctly generated the first three terms of a geometric sequence that satisfies the requirements specified in the question.
  • Teacher:The student correctly generated a geometric sequence that met the constraints defined in the question.
• Observable: 1, 4, 16. Score: 1; Evidence Value: 1.
  • Student:Right! You correctly generated the first three terms of a geometric sequence that satisfies the requirements specified in the question.
  • Teacher:The student correctly generated a geometric sequence that met the constraints defined in the question.
• Observable: 1, 5, 25. Score: 1; Evidence Value: 1.
  • Student:Right! You correctly generated the first three terms of a geometric sequence that satisfies the requirements specified in the question.
  • Teacher:The student correctly generated a geometric sequence that met the constraints defined in the question.
• Observable: 2, 6, 18. Score: 1; Evidence Value: 1.
  • Student:Right! You correctly generated the first three terms of a geometric sequence that satisfies the requirements specified in the question.
  • Teacher:The student correctly generated a geometric sequence that met the constraints defined in the question.
• Observable: 2, 8, 32. Score: 1; Evidence Value: 1.
  • Student:Right! You correctly generated the first three terms of a geometric sequence that satisfies the requirements specified in the question.
  • Teacher:The student correctly generated a geometric sequence that met the constraints defined in the question.
• Observable: 2, 10, 50. Score: 1; Evidence Value: 1.
  • Student:Right! You correctly generated the first three terms of a geometric sequence that satisfies the requirements specified in the question.
  • Teacher:The student correctly generated a geometric sequence that met the constraints defined in the question.
• Observable: 3, 9, 27. Score: 1; Evidence Value: 1.
  • Student:Right! You correctly generated the first three terms of a geometric sequence that satisfies the requirements specified in the question.
  • Teacher:The student correctly generated a geometric sequence that met the constraints defined in the question.
• Observable: 3, 12, 48. Score: 1; Evidence Value: 1.
  • Student:Right! You correctly generated the first three terms of a geometric sequence that satisfies the requirements specified in the question.
  • Teacher:The student correctly generated a geometric sequence that met the constraints defined in the question.
• Observable: 3, 15, 75. Score: 1; Evidence Value: 1.
  • Student:Right! You correctly generated the first three terms of a geometric sequence that satisfies the requirements specified in the question.
  • Teacher:The student correctly generated a geometric sequence that met the constraints defined in the question.
• Observable: 1, 4, 7. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. The first term is correct, but it looks like you added 3 to each term instead of multiplying by 3. The example you generated is still a sequence, but it is an arithmetic sequence rather than than a geometric sequence.
  • Teacher:The student may not understand the distinction between arithmetic and geometric sequences.
• Observable: 1, 5, 9. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. The first term is correct, but it looks like you added 4 to each term instead of multiplying by 4. The example you generated is still a sequence, but it is an arithmetic sequence rather than than a geometric sequence.
  • Teacher:The student may not understand the distinction between arithmetic and geometric sequences.
• Observable: 1, 6, 11. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. The first term is correct, but it looks like you added 5 to each term instead of multiplying by 5. The example you generated is still a sequence, but it is an arithmetic sequence rather than than a geometric sequence.
  • Teacher:The student may not understand the distinction between arithmetic and geometric sequences.
• Observable: 2, 5, 8. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. The first term is correct, but it looks like you added 3 to each term instead of multiplying by 3. The example you generated is still a sequence, but it is an arithmetic sequence rather than than a geometric sequence.
  • Teacher:The student may not understand the distinction between arithmetic and geometric sequences.
• Observable: 2, 6, 10. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. The first term is correct, but it looks like you added 4 to each term instead of multiplying by 4. The example you generated is still a sequence, but it is an arithmetic sequence rather than than a geometric sequence.
  • Teacher:The student may not understand the distinction between arithmetic and geometric sequences.
• Observable: 2, 7, 12. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. The first term is correct, but it looks like you added 5 to each term instead of multiplying by 5. The example you generated is still a sequence, but it is an arithmetic sequence rather than than a geometric sequence.
  • Teacher:The student may not understand the distinction between arithmetic and geometric sequences.
• Observable: 3, 6, 9. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. The first term is correct, but it looks like you added 3 to each term instead of multiplying by 3. The example you generated is still a sequence, but it is an arithmetic sequence rather than than a geometric sequence.
  • Teacher:The student may not understand the distinction between arithmetic and geometric sequences.
• Observable: 3, 7, 11. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. The first term is correct, but it looks like you added 4 to each term instead of multiplying by 4. The example you generated is still a sequence, but it is an arithmetic sequence rather than than a geometric sequence.
  • Teacher:The student may not understand the distinction between arithmetic and geometric sequences.
• Observable: 3, 8, 13. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. The first term is correct, but it looks like you added 5 to each term instead of multiplying by 5. The example you generated is still a sequence, but it is an arithmetic sequence rather than than a geometric sequence.
  • Teacher:The student may not understand the distinction between arithmetic and geometric sequences.
• Observable: 3, 3, 3. Score: 0; Evidence Value: 0.
  • Student:You are close, but your response is incorrect. You have given an example of a constant sequence, which can be thought of as a geometric sequence with a common ratio of 1 or an arithmetic sequence with a common difference of 0. But the sequence you specified does not satisfy the requirements. Perhaps you misread the question.
  • Teacher:The student generated a constant sequence, probably because of a confusion between the first term and the common ratio. It is possible the student simply misread the question.
• Observable: 3, 6, 12. Score: 0; Evidence Value: 0.
  • Student:You are very close, but your response is incorrect. You have given an example of a geometric sequence, but the sequence you specified has 3 as its first term and 2 as its common ratio Perhaps you misread the question.
  • Teacher:The student generated an example of a geometric sequence, but it was not the correct sequence. It is possible the student simply misread the question.
• Observable: 3, 9, 27. Score: 0; Evidence Value: 0.
  • Student:You are very close, but your response is incorrect. You have given an example of a geometric sequence, but the sequence you specified has 3 as its first term and 3 as its common ratio. Perhaps you misread the question.
  • Teacher:The student generated an example of a geometric sequence, but it was not the correct sequence. It is possible the student simply misread the question.
• Observable: 4, 4, 4. Score: 0; Evidence Value: 0.
  • Student:You are close, but your response is incorrect. You have given an example of a constant sequence, which can be thought of as a geometric sequence with a common ratio of 1 or an arithmetic sequence with a common difference of 0. But the sequence you specified does not satisfy the requirements. Perhaps you misread the question.
  • Teacher:The student generated a constant sequence, probably because of a confusion between the first term and the common ratio. It is possible the student simply misread the question.
• Observable: 4, 8, 16. Score: 0; Evidence Value: 0.
  • Student:You are very close, but your response is incorrect. You have given an example of a geometric sequence, but the sequence you specified has 4 as its first term and 2 as its common ratio. Perhaps you misread the question.
  • Teacher:The student generated an example of a geometric sequence, but it was not the correct sequence. It is possible the student simply misread the question.
• Observable: 4, 12, 36. Score: 0; Evidence Value: 0.
  • Student:You are very close, but your response is incorrect. You have given an example of a geometric sequence, but the sequence you specified has 4 as its first term and 3 as its common ratio. Perhaps you misread the question.
  • Teacher:The student generated an example of a geometric sequence, but it was not the correct sequence. It is possible the student simply misread the question.
• Observable: 5, 5, 5. Score: 0; Evidence Value: 0.
  • Student:You are close, but your response is incorrect. You have given an example of a constant sequence, which can be thought of as a geometric sequence with a common ratio of 1 or an arithmetic sequence with a common difference of 0. But the sequence you specified does not satisfy the requirements. Perhaps you misread the question.
  • Teacher:The student generated a constant sequence, probably because of a confusion between the first term and the common ratio. It is possible the student simply misread the question.
• Observable: 5, 10, 20. Score: 0; Evidence Value: 0.
  • Student:You are very close, but your response is incorrect. You have given an example of a geometric sequence, but the sequence you specified has 5 as its first term and 2 as its common ratio. Perhaps you misread the question.
  • Teacher:The student generated an example of a geometric sequence, but it was not the correct sequence. It is possible the student simply misread the question.
• Observable: 5, 15, 45. Score: 0; Evidence Value: 0.
  • Student:You are very close, but your response is incorrect. You have given an example of a geometric sequence, but the sequence you specified has 5 as its first term and 3 as its common ratio. Perhaps you misread the question.
  • Teacher:The student generated an example of a geometric sequence, but it was not the correct sequence. It is possible the student simply misread the question.
• Observable: . Score: 0; Evidence Value: 0.
  • Student:Sorry, that was incorrect. To start this problem, enter a number between 1 and 3 (1, 2, and 3 are your choices). To get the next number, choose a multiplier between 3 and 5 inclusive, and multiply your first number by it. Your third number is found by taking your second number and multiplying it by the same multiplier used before. Suppose you chose 1 as your starting term, and 4 as your multiplier. An example of a sequence that fits the constraints would be: 1, 4, 16.
  • Teacher:The student did not give an example of a sequence that satisfied the constraints as defined in the question.

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