Which explicit rule is correct for the sequence (5,16,33,56,\ldots)?
Answer and explanation
Correct answer: \(a_n=3n^2+2n\)
The correct rule is \(a_n=3n^2+2n\). Checking it gives \(a_1=3+2=5\), \(a_2=12+4=16\), and \(a_3=27+6=33\). The linear rule \(11n-6\) may match the first two terms, but for \(n=3\) it gives 27, not 33. In an exam, test an explicit rule with at least three terms.
Frequently asked questions
What is the correct answer to this question?
\(a_n=3n^2+2n\)
Why is this the correct answer?
The correct rule is \(a_n=3n^2+2n\). Checking it gives \(a_1=3+2=5\), \(a_2=12+4=16\), and \(a_3=27+6=33\). The linear rule \(11n-6\) may match the first two terms, but for \(n=3\) it gives 27, not 33. In an exam, test an explicit rule with at least three terms.
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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