What is the (n)th term of the sequence (3,13,33,63,103,\ldots)?
Answer and explanation
Correct answer: \(5n^2-5n+3\)
The first differences are \(10,20,30,40\), and their second differences are constantly \(10\). Therefore, the sequence has a quadratic nth term whose \(n^2\) coefficient is \(10/2=5\). Substituting \(n=1,2,3\) in \(a_n=5n^2-5n+3\) gives \(3,13,33\), so it is correct. In option B, the sign of the linear term is incorrect. Exam tip: for a constant second difference, the leading coefficient of a quadratic term is half the second difference.
Frequently asked questions
What is the correct answer to this question?
\(5n^2-5n+3\)
Why is this the correct answer?
The first differences are \(10,20,30,40\), and their second differences are constantly \(10\). Therefore, the sequence has a quadratic nth term whose \(n^2\) coefficient is \(10/2=5\). Substituting \(n=1,2,3\) in \(a_n=5n^2-5n+3\) gives \(3,13,33\), so it is correct. In option B, the sign of the linear term is incorrect. Exam tip: for a constant second difference, the leading coefficient of a quadratic term is half the second difference.
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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