Which geometric progression has first term \(6\) and common ratio \(4\)?
Answer and explanation
Correct answer: \((6,24,96,384,\ldots)\)
For a geometric progression, the first term must equal the stated initial value and each following term must be obtained by multiplying by the common ratio. Starting with 6 and multiplying repeatedly by 4 gives \(6\times4=24\), \(24\times4=96\), and \(96\times4=384\). Therefore option A satisfies both conditions exactly. Option B has ratio 2 and starts with 4. Option C has a constant difference of 4, so it is arithmetic rather than geometric. Option D has the correct ratio but starts with 24, which is already the second term of the required progression.
Frequently asked questions
What is the correct answer to this question?
\((6,24,96,384,\ldots)\)
Why is this the correct answer?
For a geometric progression, the first term must equal the stated initial value and each following term must be obtained by multiplying by the common ratio. Starting with 6 and multiplying repeatedly by 4 gives \(6\times4=24\), \(24\times4=96\), and \(96\times4=384\). Therefore option A satisfies both conditions exactly. Option B has ratio 2 and starts with 4. Option C has a constant difference of 4, so it is arithmetic rather than geometric. Option D has the correct ratio but starts with 24, which is already the second term of the required progression.
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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