Is the sequence (3, 6, 12, 24, ...) a geometric progression?
Answer and explanation
Correct answer: Yes, the common ratio is 2
A sequence is a geometric progression when the ratio of each term to the preceding term is constant. Check the consecutive quotients: 6 divided by 3 equals 2, 12 divided by 6 equals 2, and 24 divided by 12 equals 2. Because every checked ratio is the same, the sequence is geometric and its common ratio is 2. Hence option A is correct. Option B confuses the ratio with the first term or with an unrelated multiplier. Option C is false because the ratios are equal, and option D is false because the terms are increasing, not decreasing. The repeated multiplication by 2 is the defining feature here.
Frequently asked questions
What is the correct answer to this question?
Yes, the common ratio is 2
Why is this the correct answer?
A sequence is a geometric progression when the ratio of each term to the preceding term is constant. Check the consecutive quotients: 6 divided by 3 equals 2, 12 divided by 6 equals 2, and 24 divided by 12 equals 2. Because every checked ratio is the same, the sequence is geometric and its common ratio is 2. Hence option A is correct. Option B confuses the ratio with the first term or with an unrelated multiplier. Option C is false because the ratios are equal, and option D is false because the terms are increasing, not decreasing. The repeated multiplication by 2 is the defining feature here.
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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