a student wrote the first three values in a geometric sequence as shown below.

$f, g, h, \ldots$

which of the following shows the correct relationship between these terms?

$f - g = g - h$

$fg = gh$

$h = \frac{g}{f}$

$h = \frac{g^2}{f}$

Question

a student wrote the first three values in a geometric sequence as shown below.

$f, g, h, \ldots$

which of the following shows the correct relationship between these terms?

$f - g = g - h$

$fg = gh$

$h = \frac{g}{f}$

$h = \frac{g^2}{f}$

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", "Common Ratio" ] } ## Define the common ratio Using the *Geometric Sequences* and *Common Ratio* knowledge points $$ r = \frac{g}{f} = \frac{h}{g} $$ ## Solve for h Using the *Algebraic Simplification* knowledge point $$ \begin{aligned} \frac{h}{g} &= \frac{g}{f} \ h &= \frac{g^2}{f} \end{aligned} $$

(A) $f - g = g - h$

(B) $fg = gh$

(C) $h = \frac{g}{f}$

(D) $h = \frac{g^2}{f}$

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

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Question

Explanation:

Define the common ratio

Solve for h

Answer: