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In an A.P if the mth term is n and the nth term is m,where m is not equal to n,Find the pth term.
We have a m = a + (m – 1) d = n,      ............. (i)
and
an = a + (n – 1) d = m             ................(ii)
Solving (1) and (2), we get
(m – n) d = n – m, or d = – 1,   ...............(iii)
and
a=n+m–1                                ...........(iv)
Therefore
a p = a + (p – 1)d
= n + m – 1 + ( p – 1) (–1) = n + m – p
Hence, the pth term is n + m – p.


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