What is the value of r in the geometric progression 15, 45, 135, 405, ...?
Answer and explanation
Correct answer: 3
The governing concept is the common ratio of a geometric progression. It is calculated by dividing any term by the immediately preceding term, provided the divisor is nonzero. Using the first two terms, r = 45 ÷ 15 = 3. The same result is confirmed by 135 ÷ 45 = 3 and 405 ÷ 135 = 3, so the sequence is consistently geometric. Therefore option B is correct. Option A does not reproduce the next term, option C would give 75 after 15, and option D confuses the first term with the ratio. Checking more than one pair also verifies the answer.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The governing concept is the common ratio of a geometric progression. It is calculated by dividing any term by the immediately preceding term, provided the divisor is nonzero. Using the first two terms, r = 45 ÷ 15 = 3. The same result is confirmed by 135 ÷ 45 = 3 and 405 ÷ 135 = 3, so the sequence is consistently geometric. Therefore option B is correct. Option A does not reproduce the next term, option C would give 75 after 15, and option D confuses the first term with the ratio. Checking more than one pair also verifies the answer.
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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