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{ "quality": "blurry", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Arithmetic Sequences", "Slope Formula" ], "new_concepts": [], "current_concepts": [ "Arithmetic Sequences", "Slope Formula", "Arithmetic Sequence Explicit Formula" ] } ## Find the common difference Using the *Slope Formula* knowledge point $$ d = \frac{200 - 50}{2 - 1} = 150 $$ ## Write the explicit rule Using the *Arithmetic Sequences* knowledge point $$ \begin{aligned} a_n &= a_1 + (n - 1)d \ a_n &= 50 + (n - 1)150 \ a_n &= 150n - 100 \end{aligned} $$ ## Calculate points for the twenty-fourth level Using the *Arithmetic Sequences* knowledge point $$ \begin{aligned} a_{24} &= 150(24) - 100 \ a_{24} &= 3600 - 100 \ a_{24} &= 3500 \end{aligned} $$ ## Question 1 The explicit rule that describes the arithmetic sequence shown in the graph is $a_n = 150n - 100$ (or $a_n = 50 + 150(n - 1)$). ## Question 2 The video game has 24 levels in all. If the pattern shown in the graph continues, how many points would a player get for finding the hidden door on the twenty-fourth level? 3500 points { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Arithmetic Sequences" ] }

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Explanation:

Find the common difference

Write the explicit rule

Calculate points for the twenty-fourth level

Answer:

Question 1

Question 2