Item: tExplicitGeometric1b

Stem:

The first four terms of a geometric sequence are given below. Choose the algebraic expression that represents the nth term in this sequence.

3, 9, 27, 81, . . .

Options:

Key:

• Observable: 1. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. Consider the case where n = 1. The expression you selected evaluates to 3(1) + 3 = 6. But the first term in the sequence is 3, not 6, so this expression can't describe this sequence.
• Observable: 2. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. Consider the case where n = 1. The expression you selected evaluates to 8 * 3sup(1-1) = 8 * 3sup0 = 8 * 1 = 8. But the first term in the sequence is 3, not 8, so this expression can't describe this sequence.
• Observable: 3. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. Consider the case where n = 1. The expression you selected evaluates to 3sup1 + 3 = 6. But the first term in the sequence is 3, not 6, so this expression can't describe this sequence.
  • Teacher:The student got this item incorrect.
• Observable: 4. Score: 1; Evidence Value: 1.
  • Student:Right! You have identified the correct expression for the nth term.
  • Teacher:The student successfully identified the correct explicit formula for an increasing geometric sequence with integer terms.
• Observable: 5. Score: 0; Evidence Value: 0.
  • Student:Although this expression works for the first term, it is not correct. Consider the case where n = 2. Then the expression you selected evaluates to 3(2) = 6. But the 2nd term in the sequence is 9, not 6. Therefore this expression does not describe this sequence. It is always a good idea to check the expression with several values of n.
  • Teacher:The student got this item incorrect.

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