Is 14, 42, 126, 378, ... a geometric progression?
Answer and explanation
Correct answer: Yes, the common ratio is 3
A sequence is a geometric progression when the quotient of every term and its preceding term is constant. Here, 42 ÷ 14 = 3, 126 ÷ 42 = 3, and 378 ÷ 126 = 3. Since the same ratio occurs throughout the displayed sequence, it is a geometric progression with common ratio 3. Therefore option A is correct. Option B mistakes the first term for the common ratio. Option C uses an irrelevant condition: the terms do not need to be equal; they need to have a constant multiplicative ratio. Option D is false because the terms increase, rather than decrease, as each term is tripled.
Frequently asked questions
What is the correct answer to this question?
Yes, the common ratio is 3
Why is this the correct answer?
A sequence is a geometric progression when the quotient of every term and its preceding term is constant. Here, 42 ÷ 14 = 3, 126 ÷ 42 = 3, and 378 ÷ 126 = 3. Since the same ratio occurs throughout the displayed sequence, it is a geometric progression with common ratio 3. Therefore option A is correct. Option B mistakes the first term for the common ratio. Option C uses an irrelevant condition: the terms do not need to be equal; they need to have a constant multiplicative ratio. Option D is false because the terms increase, rather than decrease, as each term is tripled.
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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