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If mth term of an A.P. is n and nth term is m, then write its pth term.

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Here, 

am = n and 

an = m 

∴ a+(m-1)d = n and a+(n-1)d = m...(1)

 Subtracting above two equation we get 

a +(m-1)d-a-(n-1)d=n-m 

∴ md - d - nd + d = n-m 

∴ d(m - n) = n - m 

∴ d = -1 

Substituting d = -1 in a+(m-1)d = n we get 

∴ a+(m-1)(-1) = n 

∴ a - m + 1 = n 

∴ a = m  +n - 1 

Now, 

pth term is given by ap = a+(p-1)d 

= m+n-1+(p-1)(-1) 

= m+n-1-p+1 

= m + n - p

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