The mth term of an Ap is n and the nth term is n . Find the rth term

1.	The mth term of an Ap is n and the nth term is n . Find the rth term
Answer» Let a be the first term and d be the common difference of the given AP. Then, in general the mth and nth terms can be written as\xa0Tm = a + (m - 1) d and Tn = a + (n - 1)d respectively.According to the question,we are given that,(m.Tm) = (n.Tn){tex}\\Rightarrow{/tex}\xa0m.{a + (m - 1)d} = n.{a + (n - 1)d}{tex}\\Rightarrow{/tex}\xa0a.(m - n) + {(m2 - n2) - (m - n)} . d = 0{tex}\\Rightarrow{/tex}\xa0(m - n).{a + (m + n - 1)}d.{tex}\\Rightarrow{/tex}\xa0(m - n).Tm+n = 0{tex}\\Rightarrow{/tex}Tm+n = 0 [{tex}\\because{/tex}\xa0(m-n){tex}\\neq{/tex}0].Hence, the (m + n)th term is zero.

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