Is the sequence (2, 8, 32, 128, …) a geometric progression?
Answer and explanation
Correct answer: Yes, the common ratio is 4
The governing test for a geometric progression is that the ratio of every pair of consecutive terms must be the same. Compute the ratios: 8 ÷ 2 = 4, 32 ÷ 8 = 4, and 128 ÷ 32 = 4. Since the common ratio is consistently 4, the sequence is a geometric progression. Therefore, option B is correct. Option A identifies the wrong ratio; the terms are multiplied by 4, not 2. Option C is false because all the calculated ratios agree. Option D is also false because the terms increase from 2 to 128. A sequence may be increasing or decreasing and still be geometric; equality of consecutive ratios is the decisive condition.
Frequently asked questions
What is the correct answer to this question?
Yes, the common ratio is 4
Why is this the correct answer?
The governing test for a geometric progression is that the ratio of every pair of consecutive terms must be the same. Compute the ratios: 8 ÷ 2 = 4, 32 ÷ 8 = 4, and 128 ÷ 32 = 4. Since the common ratio is consistently 4, the sequence is a geometric progression. Therefore, option B is correct. Option A identifies the wrong ratio; the terms are multiplied by 4, not 2. Option C is false because all the calculated ratios agree. Option D is also false because the terms increase from 2 to 128. A sequence may be increasing or decreasing and still be geometric; equality of consecutive ratios is the decisive condition.
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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