Which is the (n)th term of the sequence (2,7,14,23,34,\ldots)?
Answer and explanation
Correct answer: \(n^2+2n-1\)
The consecutive differences are \(5,7,9,11\), increasing by 2, so the rule is quadratic. Using \(a_n=n^2+2n-1\) gives \(a_1=2\), \(a_2=7\), \(a_3=14\), and \(a_4=23\). Although \(n^2+1\) gives the first term as 2, it gives the second term as 5, not 7. Exam tip: test an nth-term formula with at least the first two or three terms.
Frequently asked questions
What is the correct answer to this question?
\(n^2+2n-1\)
Why is this the correct answer?
The consecutive differences are \(5,7,9,11\), increasing by 2, so the rule is quadratic. Using \(a_n=n^2+2n-1\) gives \(a_1=2\), \(a_2=7\), \(a_3=14\), and \(a_4=23\). Although \(n^2+1\) gives the first term as 2, it gives the second term as 5, not 7. Exam tip: test an nth-term formula with at least the first two or 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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