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# Massachusetts Comprehensive Assessment System

 Question 36: 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: CCSS.Math.Content.HSF-BF.A.2 - Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* Livy and Zack are writing arithmetic sequences. The first three terms of Livy's sequence are shown below.4, 7, 10, . . .What is the common difference for Livy's sequence? Show or explain how you got your answer.Write an expression that can be used to find the nth term of Livy's sequence.The nth term of Zack's sequence is three times the nth term of Livy's sequence.What is the 5th term of Zack's sequence? Show or explain how you got your answer.Write an expression that represents the difference of the nth term of Zack's sequence and the nth term of Livy'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 sequences with an explicit formula. The student writes an expression that represents the difference of the nth terms of two sequences.
4
3 The student response demonstrates a good understanding of the Algebra and Functions concepts involved in writing arithmetic 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 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 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 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: