Is (12,36,108,324,\ldots) a geometric progression?
Answer and explanation
Correct answer: Yes common ratio is (3)
The defining feature of a geometric progression is a constant multiplier between consecutive terms. To test the sequence, divide each term by the preceding term. If the same quotient is obtained each time, the sequence is geometric, and that quotient is its common ratio.
For this sequence, \(36\div12=3\), \(108\div36=3\), and \(324\div108=3\). Thus every term is obtained by multiplying the previous term by 3. The sequence is therefore a geometric progression with common ratio 3, so option A is correct. The number 12 is the first term, while the sequence is increasing, not decreasing.
Frequently asked questions
What is the correct answer to this question?
Yes common ratio is (3)
Why is this the correct answer?
The defining feature of a geometric progression is a constant multiplier between consecutive terms. To test the sequence, divide each term by the preceding term. If the same quotient is obtained each time, the sequence is geometric, and that quotient is its common ratio.
For this sequence, \(36\div12=3\), \(108\div36=3\), and \(324\div108=3\). Thus every term is obtained by multiplying the previous term by 3. The sequence is therefore a geometric progression with common ratio 3, so option A is correct. The number 12 is the first term, while the sequence is increasing, not decreasing.
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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