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Show that the sum of the (m+n)^th and (m-n)^th terms of an A.P is equal to twice the m^th term.

1 Answers

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

add both

T_m+n+T_m-n=2a+(m+n-1+m-n-1)d
=2a+2(m-1)d
=2T_m

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