What is the general term of the sequence (3, 6, 9, 12, …)?
Answer and explanation
Correct answer: aₙ = 3n
The governing concept is an explicit or general rule, which expresses a term directly in terms of its position n rather than using the preceding term. The sequence 3, 6, 9, 12 consists of successive multiples of 3. Testing aₙ = 3n gives a₁ = 3(1) = 3, a₂ = 3(2) = 6, a₃ = 3(3) = 9 and a₄ = 3(4) = 12, so it matches every displayed term. Therefore option C is correct. The rule n + 3 gives 4 as its first term, 2n gives 2 as its first term, and 3n + 1 gives 4 as its first term. Since each of these already fails at n = 1, none can represent the sequence.
Frequently asked questions
What is the correct answer to this question?
aₙ = 3n
Why is this the correct answer?
The governing concept is an explicit or general rule, which expresses a term directly in terms of its position n rather than using the preceding term. The sequence 3, 6, 9, 12 consists of successive multiples of 3. Testing aₙ = 3n gives a₁ = 3(1) = 3, a₂ = 3(2) = 6, a₃ = 3(3) = 9 and a₄ = 3(4) = 12, so it matches every displayed term. Therefore option C is correct. The rule n + 3 gives 4 as its first term, 2n gives 2 as its first term, and 3n + 1 gives 4 as its first term. Since each of these already fails at n = 1, none can represent the sequence.
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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