Why is the sequence (2, 4, 6, 8, ...) not a geometric progression?
Answer and explanation
Correct answer: The ratios are not equal
The defining condition for a geometric progression is a constant multiplicative ratio between consecutive terms. For this sequence, the first two relevant ratios are 4 divided by 2, which is 2, and 6 divided by 4, which is 3/2. The next ratio, 8 divided by 6, is 4/3. Since 2, 3/2, and 4/3 are not equal, the sequence is not geometric. Therefore option C is correct. The sequence is instead an arithmetic progression because its consecutive difference is constant: 4 - 2 = 2, 6 - 4 = 2, and 8 - 6 = 2. Options A, B, and D are merely observations and do not determine whether a sequence is geometric.
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What is the correct answer to this question?
The ratios are not equal
Why is this the correct answer?
The defining condition for a geometric progression is a constant multiplicative ratio between consecutive terms. For this sequence, the first two relevant ratios are 4 divided by 2, which is 2, and 6 divided by 4, which is 3/2. The next ratio, 8 divided by 6, is 4/3. Since 2, 3/2, and 4/3 are not equal, the sequence is not geometric. Therefore option C is correct. The sequence is instead an arithmetic progression because its consecutive difference is constant: 4 - 2 = 2, 6 - 4 = 2, and 8 - 6 = 2. Options A, B, and D are merely observations and do not determine whether a sequence is geometric.
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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