What is the value of \(r\) in the geometric progression \((4,12,36,108,\ldots)\)?
Answer and explanation
Correct answer: 3
In a geometric progression, the common ratio \(r\) is found by dividing any nonzero term by the term immediately before it. Using the first two terms gives \(r=\frac{12}{4}=3\). This is confirmed by the next pairs: \(\frac{36}{12}=3\) and \(\frac{108}{36}=3\). Therefore, option B is correct. Option A would describe doubling, option C would require each term to be four times the previous one, and option D would require a factor of six. Since every displayed transition is multiplication by 3, the sequence is consistent with \(r=3\).
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 \(r\) is found by dividing any nonzero term by the term immediately before it. Using the first two terms gives \(r=\frac{12}{4}=3\). This is confirmed by the next pairs: \(\frac{36}{12}=3\) and \(\frac{108}{36}=3\). Therefore, option B is correct. Option A would describe doubling, option C would require each term to be four times the previous one, and option D would require a factor of six. Since every displayed transition is multiplication by 3, the sequence is consistent with \(r=3\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Geometric Progression.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
