If m times the 'm'th term of an A.P. be equal to n times the 'n'th term, show that is (m+n)th term is zero.

Answer 1

term(m) = a + (m-1)d
term(n) = a + (n-1)d

m(a + (m-1)d ) = n(a + (n-1)d )
m(a + dm - d) = n(a + dn - d)
am + dm^2 - dm = an + dn^2 - nd
am - an = dn^2 - dm^2 + dm - dn
a = (dn^2 - dm^2 + dm - dn)/(m-n)

term(m+n) = a + (m+n-1)d
= a + md + nd - d
= (dn^2 - dm^2 + dm - dn)/(m-n) + md + nd - d
= [ dn^2 - dm^2 + dm - dn + dm^2 - mnd + dmn - dn^2 - dm + dn] / (m-n)
= 0/(m-n)
= 0

Yeahhh

Answer 2

S2