If m times the mth term of an AP is equal to n times its nt

Question

If m times the

m^{t h}

term of an AP is equal to n times its

n^{t h}

term, find the

(m + n)^{t h}

term of that AP. Given that m is not equal to n.

Answer: Option D
:
D
m(a + (m-1)d) = n(a + (n-1)d)
am + (m-1)dm = an + (n-1)nd
a(m-n) + d[m(m-1) - n(n-1)] = 0
(m-n)(a + d(m+n-1)) = 0
m is not equal to n.
a + d(m+n-1) = 0
(m+n) term is zero.

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