If (3, 15, 75, □, …) is a geometric progression, what term fills the blank?
Answer and explanation
Correct answer: 375
The governing property is a constant common ratio between consecutive terms. From the first two terms, r = 15 ÷ 3 = 5; this is confirmed because 75 ÷ 15 = 5. To obtain the missing fourth term, multiply the third term by the same ratio: 75 × 5 = 375. Thus option C is correct. Option A would multiply 75 by 3, not by the established ratio; option B does not preserve the ratio; and option D would require a ratio of 6. Continuing a geometric progression means applying the same multiplier at every step, not adding a fixed number or choosing a convenient larger value.
Frequently asked questions
What is the correct answer to this question?
375
Why is this the correct answer?
The governing property is a constant common ratio between consecutive terms. From the first two terms, r = 15 ÷ 3 = 5; this is confirmed because 75 ÷ 15 = 5. To obtain the missing fourth term, multiply the third term by the same ratio: 75 × 5 = 375. Thus option C is correct. Option A would multiply 75 by 3, not by the established ratio; option B does not preserve the ratio; and option D would require a ratio of 6. Continuing a geometric progression means applying the same multiplier at every step, not adding a fixed number or choosing a convenient larger value.
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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