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Question

If m times mth term of an A.P. is equal to n times its nth term find its (m+n)th term

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Solution

Given,

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

am+(m2m)d=an+(n2n)d

a(mn)+d[(m2m)(n2n)]=0

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

(mn)[a+d(m+n1)]=0

mn0

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

Now,

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

=0

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