Item: tRecursiveRuleGeometric2a

Stem:

Let a1, a2, a3, ..., an, ... be a sequence of integers. The first four terms of the sequence are given below.

-6, -24, -96, -384, . . .

Select the correct rule for finding the (n+1)th term from the nth term.

Options:

Key:

• Observable: 2. Score: 1; Evidence Value: 1.
  • Student:Right! Good job. Starting with the second term, each term in the sequence is equal to four times the previous term.
  • Teacher:The student was able to select the correct recursive rule for generating successive terms in a decreasing geometric sequence with negative integer terms.
• Observable: 1. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. Try testing the equation you selected by substituting a few numbers. Suppose n = 1. Then an = -6. So an+1 = -6 * -6 = 36. But an+1 = a2 = -24. 36 is not equal to -24, so this cannot be the correct equation.
  • Teacher:The student was not able to select the correct recursive rule for generating successive terms in a decreasing geometric sequence with negative integer terms. The student may have confused the initial term with the common ratio.
• Observable: 3. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. Try testing the equation you selected by substituting a few numbers. Suppose n = 1. Then an = -6. So an+1 = -(-6) / 6 = 1. But an+1 = a2 = -24. 1 is not equal to -24, so this cannot be the correct equation.
  • Teacher:The student was not able to select the correct recursive rule for generating successive terms in a decreasing geometric sequence with negative integer terms.
• Observable: 4. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. Try testing the equation you selected by substituting a few numbers. Suppose n = 1. Then an = -6, and 4n-1 = 40 = 1. So an+1 = -6 * 1 = -6. But an+1 = a2 = -24. -6 is not equal to -24, so this cannot be the correct equation.
  • Teacher:The student was not able to select the correct recursive rule for generating successive terms in a decreasing geometric sequence with negative integer terms. The student may have confused the recursive rule for a geometric sequence with an explicit rule for a geometric sequence.
• Observable: 5. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. Try testing the equation you selected by substituting a few numbers. Suppose n = 1. Then an = -6. So an+1 = -4 * -6 = 24. But an+1 = a2 = -24. 24 is not equal to -24, so this cannot be the correct equation.
  • Teacher:The student was not able to select the correct recursive rule for generating successive terms in a decreasing geometric sequence with negative integer terms. The student may have difficulty with multiplicative operations involving negative numbers.

Metadata: