Which of the following expressions for \(a_n\), for every natural number \(n\), can represent the nth term of an arithmetic progression?
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Answer and explanation
Correct answer: \(a_n=4n-7\)
For option A, \(a_{n+1}-a_n=[4(n+1)-7]-(4n-7)=4\), which is constant, so it is an AP. For \(n^2-7\), the difference \(2n+1\) varies. Exam tip: \(pn+q\) form gives an AP.
Frequently asked questions
What is the correct answer to this question?
\(a_n=4n-7\)
Why is this the correct answer?
For option A, \(a_{n+1}-a_n=[4(n+1)-7]-(4n-7)=4\), which is constant, so it is an AP. For \(n^2-7\), the difference \(2n+1\) varies. Exam tip: \(pn+q\) form gives 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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