Which is the correct rule for the sequence (14,31,54,83,\ldots)?
Answer and explanation
Correct answer: \(a_n=3n^2+8n+3\)
In option A, substituting \(n=1,2,3,4\) gives \(14,31,54,83\), respectively. Therefore, the correct rule is \(a_n=3n^2+8n+3\). For example, when \(n=3\), \(a_3=3(3)^2+8(3)+3=54\). Option B also gives 14 as its first term, but it gives 29, not 31, when \(n=2\). Exam tip: verify at least the first two or three terms before selecting a general rule.
Frequently asked questions
What is the correct answer to this question?
\(a_n=3n^2+8n+3\)
Why is this the correct answer?
In option A, substituting \(n=1,2,3,4\) gives \(14,31,54,83\), respectively. Therefore, the correct rule is \(a_n=3n^2+8n+3\). For example, when \(n=3\), \(a_3=3(3)^2+8(3)+3=54\). Option B also gives 14 as its first term, but it gives 29, not 31, when \(n=2\). Exam tip: verify at least the first two or three terms before selecting a general 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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