In an arithmetic progression, if the terms at two different positions are equal, i.e. \(a_p=a_q\) where \(p\ne q\), which conclusion is necessary?
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Answer and explanation
Correct answer: The common difference is \(0\), so all terms are equal
Using \(a_p=a+(p-1)d\) and \(a_q=a+(q-1)d\) gives \((p-q)d=0\). Since \(p\ne q\), \(d=0\), so every term is equal. Exam tip: isolate the difference of indices first.
Frequently asked questions
What is the correct answer to this question?
The common difference is \(0\), so all terms are equal
Why is this the correct answer?
Using \(a_p=a+(p-1)d\) and \(a_q=a+(q-1)d\) gives \((p-q)d=0\). Since \(p\ne q\), \(d=0\), so every term is equal. Exam tip: isolate the difference of indices first.
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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