If \((x,3x,9x,\ldots)\) is a geometric progression, what is the common ratio?
Answer and explanation
Correct answer: 3
For a geometric progression, the common ratio is the quotient of a term and the preceding term, provided the preceding term is nonzero. From the first two terms, \(r=\frac{3x}{x}=3\), assuming \(x\ne0\). The next pair confirms the same result: \(\frac{9x}{3x}=3\). Hence option C is correct. The symbol \(x\) is a variable, not the ratio itself; 2 does not describe either successive multiplication shown, and 9 is the coefficient of the third term rather than the factor between adjacent terms. The sequence follows \(x,3x,9x\) by multiplying by 3 each time.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
For a geometric progression, the common ratio is the quotient of a term and the preceding term, provided the preceding term is nonzero. From the first two terms, \(r=\frac{3x}{x}=3\), assuming \(x\ne0\). The next pair confirms the same result: \(\frac{9x}{3x}=3\). Hence option C is correct. The symbol \(x\) is a variable, not the ratio itself; 2 does not describe either successive multiplication shown, and 9 is the coefficient of the third term rather than the factor between adjacent terms. The sequence follows \(x,3x,9x\) by multiplying by 3 each time.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Geometric Progression.
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