Let a1, a2, a3,
..., an, ... be a sequence
of integers. The first four terms of the sequence are given below.
-2, 10, -50, 250, . . .
Select the correct rule for finding the (n+1)th term from the nth term.
5
Right! Good job. Starting with the second term, each term in the sequence is equal to negative five times the previous term.
The student was able to select the correct recursive rule for generating successive terms in a geometric sequence with integer terms and a negative common ratio.
1
Sorry, that's incorrect. Try testing the equation you selected by substituting a few numbers. Suppose n = 1. Then an = -2. So an+1 = -2/2 = -1. But an+1 = a2 = 10. -1 is not equal to 10, so this cannot be the correct equation.
The student was not able to select the correct recursive rule for generating successive terms in a geometric sequence with integer terms and a negative common ratio.
2
Sorry, that's incorrect. Try testing the equation you selected by substituting a few numbers. Suppose n = 1. Then an = -2, and -5 n-1 = -50 = 1. So an+1 = -2 * 1 = -2. But an+1 = a2 = 10. -2 is not equal to 10, so this cannot be the correct equation.
The student was not able to select the correct recursive rule for generating successive terms in a geometric sequence with integer terms and a negative common ratio. The student may have confused the recursive rule for a geometric sequence with an explicit rule for a geometric sequence.
3
Sorry, that's incorrect. Try testing the equation you selected by substituting a few numbers. Suppose n = 1. Then an = -2. So an+1 = -5 + -2 = -7. But an+1 = a2 = 10. -7 is not equal to 10, so this cannot be the correct equation.
The student was not able to select the correct recursive rule for generating successive terms in a geometric sequence with integer terms and a negative common ratio. The student may be confusing multiplicative and additive operations, or confusing the rules for geometric sequences with those for arithemetic sequences.
4
Sorry, that's incorrect. Try testing the equation you selected by substituting a few numbers. Suppose n = 1. Then an = -2. So an+1 = -2 * -2 = 4. But an+1 = a2 = 10. 4 is not equal to 10, so this cannot be the correct equation.
The student was not able to select the correct recursive rule for generating successive terms in a geometric sequence with integer terms and a negative common ratio. The student may have confused the initial term with the common ratio.
RecursiveRuleGeometric