What is the general term of the sequence 9, 26, 55, 96, …?
Answer and explanation
Correct answer: aₙ = 6n² − n + 4
The governing concept is identifying a quadratic explicit rule. The first differences are 17, 29 and 41; their second differences are 12 and 12, so a quadratic expression is appropriate. Test option A directly: a₁ = 6(1)² − 1 + 4 = 9; a₂ = 6(4) − 2 + 4 = 26; a₃ = 6(9) − 3 + 4 = 55; and a₄ = 6(16) − 4 + 4 = 96. It matches every listed term, so A is correct. Option B is linear and gives 18 at n = 2, option C gives 26 at n = 2 but 43 at n = 3, and option D gives 9 at n = 1 but 28 at n = 2. Constant second differences support the quadratic rule.
Frequently asked questions
What is the correct answer to this question?
aₙ = 6n² − n + 4
Why is this the correct answer?
The governing concept is identifying a quadratic explicit rule. The first differences are 17, 29 and 41; their second differences are 12 and 12, so a quadratic expression is appropriate. Test option A directly: a₁ = 6(1)² − 1 + 4 = 9; a₂ = 6(4) − 2 + 4 = 26; a₃ = 6(9) − 3 + 4 = 55; and a₄ = 6(16) − 4 + 4 = 96. It matches every listed term, so A is correct. Option B is linear and gives 18 at n = 2, option C gives 26 at n = 2 but 43 at n = 3, and option D gives 9 at n = 1 but 28 at n = 2. Constant second differences support the quadratic 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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