Q. 12

In an AP, the pth term is q and (p + q)th term is 0. Show that its qth term is p.

Answer :

Given: pth term is q and (p + q)th term is 0.


To prove: qth term is p.


pth term is given by


q = a + (p - 1) × d……equation1


(p + q)th term is given by


0 = a + (p + q - 1) × d


0 = a + (p - 1) × d + q × d


Using equation1


0 = q + q × d


d = - 1


Put in equation1 we get


a = q + p - 1


qth term is


q + p - 1 + (q - 1) × ( - 1)


p


Hence proved.


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