What is the general term of the sequence (3/2, 3, 9/2, 6, …)?
Answer and explanation
Correct answer: aₙ = 3n/2
The terms are consecutive multiples of 3/2. Substituting the position n gives a₁ = (3/2)×1 = 3/2, a₂ = (3/2)×2 = 3, a₃ = (3/2)×3 = 9/2, and a₄ = (3/2)×4 = 6. Therefore the explicit rule is aₙ = 3n/2, so option B is correct. This also follows from the arithmetic-sequence formula: the first term is 3/2 and the common difference is 3/2, giving aₙ = 3/2 + (n − 1)(3/2) = 3n/2. Option A decreases the scale by dividing n by 3, while options C and D produce 2 and 3 for the first term instead of 3/2.
Frequently asked questions
What is the correct answer to this question?
aₙ = 3n/2
Why is this the correct answer?
The terms are consecutive multiples of 3/2. Substituting the position n gives a₁ = (3/2)×1 = 3/2, a₂ = (3/2)×2 = 3, a₃ = (3/2)×3 = 9/2, and a₄ = (3/2)×4 = 6. Therefore the explicit rule is aₙ = 3n/2, so option B is correct. This also follows from the arithmetic-sequence formula: the first term is 3/2 and the common difference is 3/2, giving aₙ = 3/2 + (n − 1)(3/2) = 3n/2. Option A decreases the scale by dividing n by 3, while options C and D produce 2 and 3 for the first term instead of 3/2.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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