If p and q are constants, which of the following forms of the nth term guarantees that the sequence is an arithmetic progression?
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Answer and explanation
Correct answer: \(a_n=pn+q\)
For \(a_n=pn+q\), \(a_{n+1}-a_n=[p(n+1)+q]-(pn+q)=p\), a constant. Hence it is an AP. In \(pn^2+q\), the difference changes with n. Exam tip: a linear nth-term form indicates an AP.
Frequently asked questions
What is the correct answer to this question?
\(a_n=pn+q\)
Why is this the correct answer?
For \(a_n=pn+q\), \(a_{n+1}-a_n=[p(n+1)+q]-(pn+q)=p\), a constant. Hence it is an AP. In \(pn^2+q\), the difference changes with n. Exam tip: a linear nth-term form indicates 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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