Item: tExplicitRecursiveRuleArithmetic3a
Stem:
Let a1, a2, a3, ...,
an, ... be a sequence of positive numbers,
where a1=1, and an+1= an + 4.
Which of the following represents the nth term
in the sequence?
Options:
4n - 3
4n - 1
4n
4n + 1
4n + 4
Key:
- Observable: 1.
Score: 1;
Evidence Value: 1.
-
Student:Right!
-
Teacher:The student got this item correct.
- Observable: 2.
Score: 0;
Evidence Value: 0.
-
Student:Sorry, that was incorrect. The sequence given in the problem started with 1 and had a common difference of 4.
That sequence is: 1, 5, 9, 13 . . . A good approach to solving these kinds of problems is to
generate the sequence and then test your rule against it.
-
Teacher:The student probably didn't generate the sequence first.
- Observable: 3.
Score: 0;
Evidence Value: 0.
-
Student:Sorry, that was incorrect. The sequence given in the problem started with 1 and had a common difference of 4.
That sequence is: 1, 5, 9, 13 . . . A good approach to solving these kinds of problems is to
generate the sequence and then test your rule against it.
-
Teacher:The student probably didn't generate the sequence first.
- Observable: 4.
Score: 0;
Evidence Value: 0.
-
Student:Sorry, that was incorrect. The sequence given in the problem started with 1 and had a common difference of 4.
That sequence is: 1, 5, 9, 13 . . . A good approach to solving these kinds of problems is to
generate the sequence and then test your rule against it.
-
Teacher:The student probably didn't generate the sequence first.
- Observable: 5.
Score: 0;
Evidence Value: 0.
-
Student:Sorry, that was incorrect. The sequence given in the problem started with 1 and had a common difference of 4.
That sequence is: 1, 5, 9, 13 . . . A good approach to solving these kinds of problems is to
generate the sequence and then test your rule against it.
-
Teacher:Could be that the + 4 is taken from the recursive rule in the problem.
Metadata:
Item Node: tExplicitRecursiveRuleArithmetic3a,
Difficulty: 3.
Proficiencies: ExplicitArithmetic,
RecursiveRuleArithmetic.