ap question.........
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NOTE: This question came in our pre board exam!!!!
ATP,
m [ a+(m-1)d ] = n [ a+(n-1)d ]
am+dm(m-1)=an+dn(n-1)
am-an+dm(m-1)-dn(n-1)=0
a(m-n)+d(m²-m-n²+n)=0
a(m-n)+d[(m+n)(m-n)-1(m-n)]=0
a(m-n)+d(m-n)(m+n-1)=0
(m-n)(a+(m+n-1)d)=0
m=n or a+(m-n)d=0
But m≠n
thus,'
a+(m-1)d=0
or m+n th term is 0.
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Answer:
(m+n)th term = 0 will be proved.
proof in the attachment.
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