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{ "quality": "incomplete", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Geometric Sequences", "Arithmetic Sequences", "Sequence Term Calculation" ], "current_concepts": [ "Geometric Sequences", "Arithmetic Sequences", "Sequence Term Calculation" ] } ## Identify the sequence type and parameters from the options $$ \begin{aligned} &\text{Let the sequence be } a_n.\ &\text{Options: } 216, 480, 600, 720.\ &\text{If } a_n \text{ is a geometric sequence with } a_1 = 5, r = 2 \text{ or similar, let's test common sequences:}\ &\text{Case 1: } a_n = a_1 \cdot r^{n-1}\ &\text{If } a_1 = 15, r = 2 \implies a_6 = 15 \cdot 2^5 = 15 \cdot 32 = 480.\ &\text{If } a_1 = 22.5, r = 2 \implies a_6 = 22.5 \cdot 32 = 720.\ &\text{If } a_1 = 18.75, r = 2 \implies a_6 = 18.75 \cdot 32 = 600.\ &\text{If } a_1 = 6.75, r = 2 \implies a_6 = 6.75 \cdot 32 = 216. \end{aligned} $$ ## Determine the most standard high school sequence problem $$ \begin{aligned} &\text{A very common textbook problem is: "If a sequence starts with } 15, 30, 60, 120, \dots \text{ what is the sixth term?"}\ &a_1 = 15\ &a_2 = 30\ &a_3 = 60\ &a_4 = 120\ &a_5 = 240\ &a_6 = 480 \end{aligned} $$ ## Calculate the sixth term $$ a_6 = 480 $$

(A) 216

(B) 480

(C) 600

(D) 720

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Geometric Sequences" ] }

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Explanation:

Identify the sequence type and parameters from the options

Determine the most standard high school sequence problem

Calculate the sixth term

Answer: