What is the common ratio in the sequence (2, 6, 18, 54, ...)?
Answer and explanation
Correct answer: 3
The governing concept for a geometric progression is a constant ratio between every pair of consecutive terms. To find that ratio, divide a term by the term immediately before it. Here, 6 divided by 2 equals 3; 18 divided by 6 also equals 3; and 54 divided by 18 again equals 3. Since the quotient remains constant, the common ratio is r = 3. Therefore option B is correct. Option A is the first term, not the ratio. Option C is obtained by confusing multiplication or subtraction with division, and option D does not describe the relationship between any consecutive terms. The sequence is geometric because each term is three times the preceding term.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The governing concept for a geometric progression is a constant ratio between every pair of consecutive terms. To find that ratio, divide a term by the term immediately before it. Here, 6 divided by 2 equals 3; 18 divided by 6 also equals 3; and 54 divided by 18 again equals 3. Since the quotient remains constant, the common ratio is r = 3. Therefore option B is correct. Option A is the first term, not the ratio. Option C is obtained by confusing multiplication or subtraction with division, and option D does not describe the relationship between any consecutive terms. The sequence is geometric because each term is three times the preceding term.
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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