If the first term of a geometric progression is 40 and the common ratio is 1/2, what is the second term?
Answer and explanation
Correct answer: 20
The governing rule is a₂ = a₁r: to obtain the next term of a geometric progression, multiply the current term by the common ratio. Here a₁ = 40 and r = 1/2, so a₂ = 40 × 1/2 = 20. Therefore, option B is correct. Because the ratio is a fraction less than 1, the sequence decreases, which is consistent with 40 becoming 20. Option A would result from halving 20 again, option C does not use the ratio correctly, and option D doubles the first term instead of multiplying by one-half. Careful treatment of the fraction is essential.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
The governing rule is a₂ = a₁r: to obtain the next term of a geometric progression, multiply the current term by the common ratio. Here a₁ = 40 and r = 1/2, so a₂ = 40 × 1/2 = 20. Therefore, option B is correct. Because the ratio is a fraction less than 1, the sequence decreases, which is consistent with 40 becoming 20. Option A would result from halving 20 again, option C does not use the ratio correctly, and option D doubles the first term instead of multiplying by one-half. Careful treatment of the fraction is essential.
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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