Question

what is the common ratio of the sequence below?

\\(\frac{2}{3}, \frac{1}{6}, \frac{1}{24}, \frac{1}{96}, \dots\\)

• \\(\frac{1}{9}\\)
• \\(\frac{1}{4}\\)
• \\(4\\)
• \\(9\\)

Explanation:

Identify the terms of the sequence

Using the Common Ratio knowledge point

$$ a_1 = \frac{2}{3}, \quad a_2 = \frac{1}{6}, \quad a_3 = \frac{1}{24}, \quad a_4 = \frac{1}{96} $$

Calculate the common ratio

Using the Common Ratio knowledge point

$$ r = \frac{a_2}{a_1} = \frac{\frac{1}{6}}{\frac{2}{3}} = \frac{1}{6} \times \frac{3}{2} = \frac{3}{12} = \frac{1}{4} $$

Verify with subsequent terms

Using the Common Ratio knowledge point

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Answer:

• (A) \(\frac{1}{9}\)
• (B) \(\frac{1}{4}\) (Correct answer)
• (C) \(4\)
• (D) \(9\)