fiona wrote the sequence below.

3, 12, 48, 192, ...

which of the following classifies the sequence?

arithmetic
geometric
both arithmetic and geometric
neither arithmetic nor geometric

Question

fiona wrote the sequence below.

3, 12, 48, 192, ...

which of the following classifies the sequence?

arithmetic
geometric
both arithmetic and geometric
neither arithmetic nor geometric

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Geometric Sequences", "Common Ratio" ], "new_concepts": [], "current_concepts": [ "Geometric Sequences", "Arithmetic Sequences", "Common Ratio" ] } ## Analyze the sequence pattern Using the *Geometric Sequences* and *Common Ratio* knowledge points $$ \begin{aligned} &\text{Sequence: } 3, 12, 48, 192, \dots \ &\frac{12}{3} = 4, \quad \frac{48}{12} = 4, \quad \frac{192}{48} = 4 \ &\text{Common Ratio } (r) = 4 \end{aligned} $$ ## Classify the sequence Using the *Geometric Sequences* knowledge point $$ \begin{aligned} &\text{Since each term is found by multiplying the previous term by a constant non-zero number (4),} \ &\text{the sequence is geometric.} \end{aligned} $$

arithmetic

geometric

both arithmetic and geometric

neither arithmetic nor geometric

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

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Question

Explanation:

Analyze the sequence pattern

Classify the sequence

Answer: