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.

t_m + t_n

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t_m - t_n

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t_m * t_n

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Solution

The correct option is D
0

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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