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Show that the sum of $(m+n)^{th}$ and $(m-n)^{th}$ terms of an A.P is twice its $m^{th}$ term.

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In an A.P. $n^{th}$ term = $t_n=a+(n-1)d$
$\Rightarrow\:t_{m+n}=a+(m+n-1)d$ ....(i) and
$t_{m-n}=a+(m-n-1)d.......$ (ii)
Adding (i) and (ii) we get
Hence proved.
answered Mar 27, 2014 by rvidyagovindarajan_1

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