If n times n th term is equal to m times m th term.prove that m+n th t

1.	If n times n th term is equal to m times m th term.prove 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.

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