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Question

If m times the mth term of an AP is equal to n times the nth term to prove that (m+n)th term=0

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Solution

Formula:

tn=a+(n1)d

Given,

m×tm=n×tn

m[a+(m1)d]=n[a+(n1)d]

am+(m2m)dan(n2n)d=0

a(mn)+d[(m2n2)(mn)]=0

(mn)[a+d((m+n)1)]=0

a+[(m+n)1]d=0

tm+n=0

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