Which is the (n)th term of the sequence (2,12,30,56,90,\ldots)?
Answer and explanation
Correct answer: \(4n^2-2n\)
The consecutive differences are \(12-2=10\), \(30-12=18\), \(56-30=26\), and \(90-56=34\). Their second differences are constantly \(8\), so the sequence is quadratic with coefficient \(4\) for \(n^2\). Using \(a_n=4n^2-2n\) gives \(a_1=2\), \(a_2=12\), and \(a_3=30\). Option B gives \(10\) as the second term, so it is not correct. Exam tip: verify a proposed nth-term formula using at least the first three terms.
Frequently asked questions
What is the correct answer to this question?
\(4n^2-2n\)
Why is this the correct answer?
The consecutive differences are \(12-2=10\), \(30-12=18\), \(56-30=26\), and \(90-56=34\). Their second differences are constantly \(8\), so the sequence is quadratic with coefficient \(4\) for \(n^2\). Using \(a_n=4n^2-2n\) gives \(a_1=2\), \(a_2=12\), and \(a_3=30\). Option B gives \(10\) as the second term, so it is not correct. Exam tip: verify a proposed nth-term formula using at least the first three terms.
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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