Which of the following sequences has an \(n\)th term that represents an AP with a non-zero common difference?
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Answer and explanation
Correct answer: \(a_n=7n-4\)
For \(a_n=7n-4\), \(a_{n+1}-a_n=7\), a constant non-zero value for every \(n\); hence it is an AP. Terms involving \(n^2\), \(2^n\), or \(1/n\) do not have constant consecutive differences. Exam tip: a linear form \(pn+q\) always represents an AP.
Frequently asked questions
What is the correct answer to this question?
\(a_n=7n-4\)
Why is this the correct answer?
For \(a_n=7n-4\), \(a_{n+1}-a_n=7\), a constant non-zero value for every \(n\); hence it is an AP. Terms involving \(n^2\), \(2^n\), or \(1/n\) do not have constant consecutive differences. Exam tip: a linear form \(pn+q\) always represents 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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