What is the common ratio in the sequence (4,12,36,108,\ldots)?
Answer and explanation
Correct answer: (3)
The common ratio of a geometric progression is the factor used to multiply one term to get the next term. It can be found by dividing a term by the preceding term. Using the first two terms here gives \(r=\frac{12}{4}=3\). The same factor is confirmed by \(\frac{36}{12}=3\) and \(\frac{108}{36}=3\), so the sequence is consistently geometric.
Thus the correct answer is option B. Multiplying 4 by 3 gives 12, multiplying 12 by 3 gives 36, and multiplying 36 by 3 gives 108. The values 2, 4, and 6 do not reproduce these consecutive terms: for example, a ratio of 2 would make the second term 8, not 12. The ratio is a multiplier, not the difference between terms.
Frequently asked questions
What is the correct answer to this question?
(3)
Why is this the correct answer?
The common ratio of a geometric progression is the factor used to multiply one term to get the next term. It can be found by dividing a term by the preceding term. Using the first two terms here gives \(r=\frac{12}{4}=3\). The same factor is confirmed by \(\frac{36}{12}=3\) and \(\frac{108}{36}=3\), so the sequence is consistently geometric.
Thus the correct answer is option B. Multiplying 4 by 3 gives 12, multiplying 12 by 3 gives 36, and multiplying 36 by 3 gives 108. The values 2, 4, and 6 do not reproduce these consecutive terms: for example, a ratio of 2 would make the second term 8, not 12. The ratio is a multiplier, not the difference between terms.
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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