If a geometric progression has a₁ = 12 and a₂ = 48, what is its common ratio?
Answer and explanation
Correct answer: 4
The governing concept is that the common ratio of a geometric progression is the quotient of a term by the preceding term. Because a₁ = 12 and a₂ = 48, calculate r = a₂ ÷ a₁ = 48 ÷ 12 = 4. Therefore option C is correct. This value is also consistent with the first transition: multiplying 12 by 4 gives 48. Option A would produce 24, option B would produce 36, and option D would produce 72, so none of those values connects the two given terms. The order matters: use the later term divided by the earlier term, not the reverse.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The governing concept is that the common ratio of a geometric progression is the quotient of a term by the preceding term. Because a₁ = 12 and a₂ = 48, calculate r = a₂ ÷ a₁ = 48 ÷ 12 = 4. Therefore option C is correct. This value is also consistent with the first transition: multiplying 12 by 4 gives 48. Option A would produce 24, option B would produce 36, and option D would produce 72, so none of those values connects the two given terms. The order matters: use the later term divided by the earlier term, not the reverse.
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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