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# Massachusetts Comprehensive Assessment System

 Question 17: Open-Response Reporting Category: Algebra and FunctionsStandard: 10.P.1 - Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative, recursive (e.g., Fibonacci Numbers), linear, quadratic, and exponential functional relationships. (AI.P.1) Standard: Mathematics.F.BF.1.02 - Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* Monelle started an arithmetic sequence. The first four terms of her sequence are shown below.13,    9,    5,    1, . . .What is the common difference for Monelle's sequence? Show or explain how you got your answer.What is the sixth term of Monelle's sequence? Show or explain how you got your answer.Nevin started a geometric sequence. The first four terms of his sequence are shown below.162,    54,    18,    6, . . .What is the sixth term of Nevin's sequence? Show or explain how you got your answer.Write an expression that represents the nth term of Nevin's sequence.

### Scoring Guide and Sample Student WorkSelect a score point in the table below to view the sample student response.

ScoreDescription
4 The student response demonstrates an exemplary understanding of the Algebra and Functions concepts involved in writing arithmetic and geometric sequences with an explicit formula. The student extends an arithmetic sequence and a geometric sequence.
4
3 The student response demonstrates a good understanding of the Algebra and Functions concepts involved in writing arithmetic and geometric sequences with an explicit formula. Although there is significant evidence that the student was able to recognize and apply the concepts involved, some aspect of the response is flawed. As a result, the response merits 3 points.
2 The student response demonstrates a fair understanding of the Algebra and Functions concepts involved in writing arithmetic and geometric sequences with an explicit formula. While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 2 points.
1 The student response demonstrates a minimal understanding of the Algebra and Functions concepts involved in writing arithmetic and geometric sequences with an explicit formula.
0 The student response contains insufficient evidence of an understanding of the Algebra and Functions concepts involved in writing arithmetic and geometric sequences with an explicit formula to merit any points.

Note: There are 2 sample student responses for Score Point 4.

Question 17:
Question 20:
Question 21:
Question 36:
Question 41:
Question 42: