What is the general term of the sequence (−2, −2, 0, 4, …)?
Answer and explanation
Correct answer: aₙ = n² − 3n
To identify the rule, substitute the term number n into each candidate. For option A, a₁ = 1² − 3(1) = −2, a₂ = 2² − 3(2) = −2, a₃ = 3² − 3(3) = 0, and a₄ = 4² − 3(4) = 4. These are exactly the four given terms, so aₙ = n² − 3n is correct. The rule may contain negative or zero values; that does not make it invalid. Option B produces −1, 2, 7, 14, and option C produces −2, 0, 2, 4, so neither matches the sequence. Option D gives 2, 6, 12, 20 and is also inconsistent. Testing several initial indices is a reliable way to verify an explicit sequence rule.
Frequently asked questions
What is the correct answer to this question?
aₙ = n² − 3n
Why is this the correct answer?
To identify the rule, substitute the term number n into each candidate. For option A, a₁ = 1² − 3(1) = −2, a₂ = 2² − 3(2) = −2, a₃ = 3² − 3(3) = 0, and a₄ = 4² − 3(4) = 4. These are exactly the four given terms, so aₙ = n² − 3n is correct. The rule may contain negative or zero values; that does not make it invalid. Option B produces −1, 2, 7, 14, and option C produces −2, 0, 2, 4, so neither matches the sequence. Option D gives 2, 6, 12, 20 and is also inconsistent. Testing several initial indices is a reliable way to verify an explicit sequence rule.
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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