If the sum of m term of AP is the same as the sum of its n term then show that (m+n)th term is zero

If the sum of m term of AP is the same as the sum of its n term then s

1.	If the sum of m term of AP is the same as the sum of its n term then show that (m+n)th term is zero
Answer» mam = nanm[a + (m - 1)d] = n [a + (n - 1)d]{tex} \\Rightarrow {/tex}\xa0ma + m2d - md = na + n2d - nd{tex} \\Rightarrow {/tex}\xa0a(m - n) + (m2 - n2)d - md + nd = 0{tex} \\Rightarrow {/tex}\xa0a(m - n) + (m - n) (m + n)d - (m - n)d = 0{tex} \\Rightarrow {/tex}\xa0(m - n) [a + (m + n - 1)d] = 0{tex} \\Rightarrow {/tex}\xa0a + (m + n - 1)d = 0{tex} \\Rightarrow {/tex}\xa0am+n = 0Hence proved.