Which of the following rules, where n is a natural number, cannot represent the nth term of an arithmetic progression?
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Answer and explanation
Correct answer: \(n^2-3n+2\)
The nth term of an AP is \(a_n=a+(n-1)d\), so it must be linear in n. For option B, \(a_{n+1}-a_n=2n-2\), which changes with n; hence the common difference is not constant. Exam tip: check whether the first difference is fixed.
Frequently asked questions
What is the correct answer to this question?
\(n^2-3n+2\)
Why is this the correct answer?
The nth term of an AP is \(a_n=a+(n-1)d\), so it must be linear in n. For option B, \(a_{n+1}-a_n=2n-2\), which changes with n; hence the common difference is not constant. Exam tip: check whether the first difference is fixed.
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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