Item: tExtendGeometric2a

Stem:

What is the ninth term of a geometric sequence if the third term is 36 and the fourth term is 72?

Options:

1. 144

2. 108

3. 4608

4. 2304

Key:

• Observable: 4. Score: 1; Evidence Value: 1.
  • Student:Correct, good job!
  • Teacher:The student correctly determined the 9th term of a geometric sequence.
• Observable: 1. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. The question is asking for the 9th term, not the 5th term.
  • Teacher:The student gave the next term in a geometric sequence, instead of the 9th term.
• Observable: 2. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. Perhaps you added the third and fourth terms, but this is not the correct rule to generate successive terms in the sequence. This is a geometric sequence, which means there is a common ratio between terms. For example, the sequence 2, 4, 8, 16, 32,... has a common ratio of two. To generate the next term in this sequence, you multiply the current term by two.
  • Teacher:The student added two terms of the sequence together.
• Observable: 3. Score: 0; Evidence Value: 0.
  • Student:That's incorrect, but you are close! It looks like you found the 10th term, instead of the 9th term.
  • Teacher:Student gave the 10th term.

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