In an AP, if \(a_p=a_q\) for two distinct positive integers p and q, what type of AP must it be?
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Answer and explanation
Correct answer: Constant AP
For an AP, \(a_p-a_q=(p-q)d\). Since \(p\ne q\) and \(a_p=a_q\), we get \(d=0\), so every term is equal. Exam tip: equal terms at distinct indices imply zero common difference.
Frequently asked questions
What is the correct answer to this question?
Constant AP
Why is this the correct answer?
For an AP, \(a_p-a_q=(p-q)d\). Since \(p\ne q\) and \(a_p=a_q\), we get \(d=0\), so every term is equal. Exam tip: equal terms at distinct indices imply zero common difference.
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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