show
that th
times the mth term is equal to n times the nth term of an AP. Show that (m + n)th
term is zero (m + n)

1 thought on “show<br />that th<br />times the mth term is equal to n times the nth term of an AP. Show that (m + n)th<br />term is zero (m + n)”

1. Thge general nth term of an AP is a + (n -1)d.

   From the given conditions,

   m (a + (m-1)d) = n( a + (n-1)d)
   => am + m2d – md = an + n2d – nd
   => a(m-n) + (m+n)(m-n)d – (m-n)d = 0
   => (m-n) ( a + (m+n-1)d ) = 0

   Rejecting the non-trivial case of m=n, we assume that m and n are different.
   => ( a + (m + n – 1)d ) = 0

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