Which of the following formulae does not represent the \(n\)th term of an arithmetic progression (AP) for every positive integer \(n\)?
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Answer and explanation
Correct answer: \(a_n=n^2+1\)
The general term of an AP is \(a_n=a+(n-1)d\), which is linear in \(n\). Since \(n^2+1\) contains a squared term, its consecutive differences are not constant. Exam tip: a quadratic term usually indicates that the sequence is not an AP.
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^2+1\)
Why is this the correct answer?
The general term of an AP is \(a_n=a+(n-1)d\), which is linear in \(n\). Since \(n^2+1\) contains a squared term, its consecutive differences are not constant. Exam tip: a quadratic term usually indicates that the sequence is not an AP.
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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