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}\\)

Explanation:

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

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Answer:

• (A) \(f - g = g - h\)
• (B) \(fg = gh\)
• (C) \(h = \frac{g}{f}\)
• (D) \(h = \frac{g^2}{f}\) (Correct answer)