Question

In an ap the mth term is n and nth term is m find the pth term

Answer 1

Step-by-step explanation:

Let the first term and the common difference of an AP are a and d respectively.

Given, mth term = n

a+(m-1)d = n_____(1)

and, nth term = m

a+(n-1)d =m_____(2)

Now, (1)-(2)

a+(m-1)d-{a+(n-1)d}=n-m

a-a+(m-1)d-(n-1)d =n-m

d(m-1-n+1) =n-m

d(m-n) = -(m-n)

d = (-m-n) /(m-n)

d = -1

by putting the value of d in (1) we get,

a+(m-1)( -1) =n

a-m+1 =n

a =m+n-1

therefore, pth term=a+(p-1)d

=m+n-1-p+1

=m+n-p

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