Item: tExplicitGeometric1a

Stem:

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

4, 16, 64, 256, . . .

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 4(1) + 4 = 8. But the first term in the sequence is 4, not 8, so this expression can't describe this sequence.
  • Teacher:The student got this item incorrect.
• Observable: 2. 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 4(2) = 8. But the 2nd term in the sequence is 16, not 8. 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.
• Observable: 3. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. Consider the case where n = 1. The expression you selected evaluates to 4sup1 + 4 = 8. But the first term in the sequence is 4, not 8, so this expression can't describe this sequence.
  • Teacher:The student got this item incorrect.
• Observable: 4. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. Consider the case where n = 1. The expression you selected evaluates to 3 * 4sup(1-1) = 3 * 4sup0 = 3 * 1 = 3. But the first term in the sequence is 4, not 3, so this expression can't describe this sequence.
  • Teacher:The student got this item incorrect.
• Observable: 5. 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.

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