If the first term of a geometric progression is 54 and the common ratio is 1/3, what is the second term?
Answer and explanation
Correct answer: 18
The governing concept is the term-to-term rule of a geometric progression: every term is obtained by multiplying the preceding term by the same common ratio. Therefore, the second term is found from a₂ = a₁r. Substituting the given values gives a₂ = 54 × 1/3 = 18. Thus option B is correct. Option A would result from dividing 54 by 6, not by the given ratio; option C corresponds to multiplying by 1/2; and option D incorrectly multiplies by 3. Since the ratio is less than 1, the terms decrease from 54 to 18.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
The governing concept is the term-to-term rule of a geometric progression: every term is obtained by multiplying the preceding term by the same common ratio. Therefore, the second term is found from a₂ = a₁r. Substituting the given values gives a₂ = 54 × 1/3 = 18. Thus option B is correct. Option A would result from dividing 54 by 6, not by the given ratio; option C corresponds to multiplying by 1/2; and option D incorrectly multiplies by 3. Since the ratio is less than 1, the terms decrease from 54 to 18.
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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