Which of the following given \(n\)th terms does not represent an arithmetic progression (AP)?
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Answer and explanation
Correct answer: \(a_n=n^2+2\)
The nth term of an AP is \(a_n=a+(n-1)d\), so it is linear in \(n\). In \(n^2+2\), the consecutive differences are \(3,5,7\dots\), not constant. Exam tip: check whether the first differences remain equal.
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^2+2\)
Why is this the correct answer?
The nth term of an AP is \(a_n=a+(n-1)d\), so it is linear in \(n\). In \(n^2+2\), the consecutive differences are \(3,5,7\dots\), not constant. Exam tip: check whether the first differences remain equal.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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