If an arithmetic progression satisfies $a_m=a_n$ for $m\ne n$, which statement must be true?

Question

Answer and explanation

Correct answer: The common difference is 0 and all terms of the AP are equal

Using $a_n=a+(n-1)d$, we get $(m-n)d=0$. Since $m\ne n$, $d=0$, so every term equals $a$. Exam tip: first note that the indices are distinct.

What is the correct answer to this question?

The common difference is 0 and all terms of the AP are equal

Why is this the correct answer?

Using $a_n=a+(n-1)d$, we get $(m-n)d=0$. Since $m\ne n$, $d=0$, so every term equals $a$. Exam tip: first note that the indices are distinct.

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.