If the nth term of a sequence is \(a_n=pn+q\), where \(p\) and \(q\) are constants, which of the following statements is always true?
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Answer and explanation
Correct answer: It is an AP with common difference \(p\)
\(a_{n+1}-a_n=[p(n+1)+q]-(pn+q)=p\), which is constant for every \(n\). Hence the sequence is an AP with common difference \(p\), not \(q\). Exam tip: test an AP by subtracting consecutive terms.
Frequently asked questions
What is the correct answer to this question?
It is an AP with common difference \(p\)
Why is this the correct answer?
\(a_{n+1}-a_n=[p(n+1)+q]-(pn+q)=p\), which is constant for every \(n\). Hence the sequence is an AP with common difference \(p\), not \(q\). Exam tip: test an AP by subtracting consecutive terms.
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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