What is the (n)th term of the sequence (3,8,15,24,35,\ldots)?
Answer and explanation
Correct answer: \(n^2+2n\)
The consecutive differences are 5, 7, 9, and 11, increasing by 2 each time, so the rule is quadratic. Substituting \(n=1,2,3\) in \(n^2+2n\) gives 3, 8, and 15 respectively; hence the nth term is \(n^2+2n\). The closest distractor, \(n^2+n+1\), gives 7 when \(n=2\), not 8. Exam tip: substitute the first two or three values of \(n\) to verify an nth-term formula quickly.
Frequently asked questions
What is the correct answer to this question?
\(n^2+2n\)
Why is this the correct answer?
The consecutive differences are 5, 7, 9, and 11, increasing by 2 each time, so the rule is quadratic. Substituting \(n=1,2,3\) in \(n^2+2n\) gives 3, 8, and 15 respectively; hence the nth term is \(n^2+2n\). The closest distractor, \(n^2+n+1\), gives 7 when \(n=2\), not 8. Exam tip: substitute the first two or three values of \(n\) to verify an nth-term formula quickly.
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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