Q10 of 167 Page 20

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

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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