The nth term of a sequence is \(a_n=pn+q\), where \(p\) and \(q\) are constants. Which statement about this sequence being an arithmetic progression (AP) is correct?
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Answer and explanation
Correct answer: It is an AP for every constant \(p\) and \(q\), and its common difference is \(p\).
The consecutive-term difference is \(a_{n+1}-a_n=[p(n+1)+q]-(pn+q)=p\), which is constant. Hence it is an AP for all constant \(p,q\), including \(p=0\), when it is a constant AP. Exam tip: check consecutive differences.
Frequently asked questions
What is the correct answer to this question?
It is an AP for every constant \(p\) and \(q\), and its common difference is \(p\).
Why is this the correct answer?
The consecutive-term difference is \(a_{n+1}-a_n=[p(n+1)+q]-(pn+q)=p\), which is constant. Hence it is an AP for all constant \(p,q\), including \(p=0\), when it is a constant AP. Exam tip: check consecutive differences.
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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