Why is the sequence (3, 6, 9, 12, …) not a geometric progression?
Answer and explanation
Correct answer: The ratios are not equal
A geometric progression is defined by a constant multiplicative ratio between consecutive terms. For this sequence, the first ratio is 6 ÷ 3 = 2, while the next ratio is 9 ÷ 6 = 3/2. These values are unequal, and the following ratio 12 ÷ 9 = 4/3 is different again. Hence the sequence is not geometric, so option C is correct. It is instead an arithmetic progression because the common difference is 3: 6 − 3 = 3, 9 − 6 = 3, and 12 − 9 = 3. Increasing terms do not prevent a sequence from being geometric, and being multiples of 3 or having first term 3 is irrelevant to the defining ratio.
Frequently asked questions
What is the correct answer to this question?
The ratios are not equal
Why is this the correct answer?
A geometric progression is defined by a constant multiplicative ratio between consecutive terms. For this sequence, the first ratio is 6 ÷ 3 = 2, while the next ratio is 9 ÷ 6 = 3/2. These values are unequal, and the following ratio 12 ÷ 9 = 4/3 is different again. Hence the sequence is not geometric, so option C is correct. It is instead an arithmetic progression because the common difference is 3: 6 − 3 = 3, 9 − 6 = 3, and 12 − 9 = 3. Increasing terms do not prevent a sequence from being geometric, and being multiples of 3 or having first term 3 is irrelevant to the defining ratio.
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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