The nth term of an arithmetic progression is \(a_n=pn+q\), where \(p\) and \(q\) are constants. What is the common difference of the progression?
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Answer and explanation
Correct answer: \(p\)
The common difference is \(a_{n+1}-a_n\). Here, \(a_{n+1}=p(n+1)+q=pn+p+q\), so the difference is \(p\). The constant \(q\) only shifts every term. Exam tip: identify the coefficient of \(n\).
Frequently asked questions
What is the correct answer to this question?
\(p\)
Why is this the correct answer?
The common difference is \(a_{n+1}-a_n\). Here, \(a_{n+1}=p(n+1)+q=pn+p+q\), so the difference is \(p\). The constant \(q\) only shifts every term. Exam tip: identify the coefficient of \(n\).
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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