If the nth term of a sequence is \(a_n=pn+q\), where \(p\) and \(q\) are constants, what type of sequence is it?
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Answer and explanation
Correct answer: An AP with common difference \(p\)
The difference is \(a_{n+1}-a_n=[p(n+1)+q]-(pn+q)=p\), which is constant. Hence it is an AP; \(q\) affects the first term, not the common difference. Exam tip: subtract consecutive terms to identify an AP.
Frequently asked questions
What is the correct answer to this question?
An AP with common difference \(p\)
Why is this the correct answer?
The difference is \(a_{n+1}-a_n=[p(n+1)+q]-(pn+q)=p\), which is constant. Hence it is an AP; \(q\) affects the first term, not the common difference. Exam tip: subtract consecutive terms to identify 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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