Which is the (n)th term of the sequence (15,27,41,57,75,\ldots)?
Answer and explanation
Correct answer: \(n^2+9n+5\)
The consecutive differences are 12, 14, 16, and 18; their second differences are 2, so the nth term is quadratic. For \(a_n=n^2+9n+5\), we get \(a_1=15\), \(a_2=27\), and \(a_3=41\). Hence, \(n^2+9n+5\) is correct. The close distractor \(n^2+8n+6\) gives 15 at \(n=1\), but gives 26 at \(n=2\), not 27. Exam tip: for a quadratic sequence, check both first and second differences.
Frequently asked questions
What is the correct answer to this question?
\(n^2+9n+5\)
Why is this the correct answer?
The consecutive differences are 12, 14, 16, and 18; their second differences are 2, so the nth term is quadratic. For \(a_n=n^2+9n+5\), we get \(a_1=15\), \(a_2=27\), and \(a_3=41\). Hence, \(n^2+9n+5\) is correct. The close distractor \(n^2+8n+6\) gives 15 at \(n=1\), but gives 26 at \(n=2\), not 27. Exam tip: for a quadratic sequence, check both first and second differences.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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