Which geometric progression has first term 8 and common ratio 3?
Answer and explanation
Correct answer: 8, 24, 72, 216, ...
A geometric progression with first term 8 and common ratio 3 must begin with 8, and each following term must be three times the preceding term. Option A satisfies both conditions: 24 = 8 × 3, 72 = 24 × 3, and 216 = 72 × 3. Therefore option A is correct. Option B has common ratio 3 but starts with 3 rather than 8. Option C starts with 8 but adds 3 each time, so it is arithmetic, not geometric. Option D follows ratio 3 but begins with 24, which is the second term of the required progression. Both the initial value and the multiplication rule must be checked.
Frequently asked questions
What is the correct answer to this question?
8, 24, 72, 216, ...
Why is this the correct answer?
A geometric progression with first term 8 and common ratio 3 must begin with 8, and each following term must be three times the preceding term. Option A satisfies both conditions: 24 = 8 × 3, 72 = 24 × 3, and 216 = 72 × 3. Therefore option A is correct. Option B has common ratio 3 but starts with 3 rather than 8. Option C starts with 8 but adds 3 each time, so it is arithmetic, not geometric. Option D follows ratio 3 but begins with 24, which is the second term of the required progression. Both the initial value and the multiplication rule must be checked.
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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