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2015-10-28T12:54:02+05:30

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Mth term of AP = a + (m-1)d
nth term of AP = a + (n-1)d
Given that
m time mth term = n times nth term
m[a+md-d] = n[a + nd - d]

ma + m²d - md = na + n²d - nd
ma + m²d - md -  na - n²d + nd = 0

a(m-n) + d(m²-n²) -d(m-n) = 0

taking (m-n) common and simplifying
a + d(m+n) - d = 0

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

(m+n)th term = 0

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