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?

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.