What is the common ratio in the sequence (6,18,54,162,\ldots)?
Answer and explanation
Correct answer: (3)
In a geometric progression, the common ratio is the number by which each term is multiplied to obtain the next term. Compute the quotient of consecutive terms: 18/6=3 . Checking further gives 54/18=3 and 162/54=3 , so the same multiplier is used throughout the sequence. Therefore the common ratio is r=3 .
Option C is consequently correct. The ratio is not found by subtracting terms; the differences are 12, 36, and 108, which are not constant. Nor should the first term itself be chosen as the ratio. Dividing any nonzero term by the preceding term gives the same result here, confirming that the sequence is geometric with positive ratio 3.
Frequently asked questions
What is the correct answer to this question?
(3)
Why is this the correct answer?
In a geometric progression, the common ratio is the number by which each term is multiplied to obtain the next term. Compute the quotient of consecutive terms: 18/6=3 . Checking further gives 54/18=3 and 162/54=3 , so the same multiplier is used throughout the sequence. Therefore the common ratio is r=3 .
Option C is consequently correct. The ratio is not found by subtracting terms; the differences are 12, 36, and 108, which are not constant. Nor should the first term itself be chosen as the ratio. Dividing any nonzero term by the preceding term gives the same result here, confirming that the sequence is geometric with positive ratio 3.
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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