12.In an A.P. prove that t m+n +t m-n =2t m .
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Answer:
Formula,
t
n
=a+(n−1)d
t
m+n
=a+[(m+n)−1]d
t
m−n
=a+[(m−n)−1]d
t
m+n
−t
m−n
=a+[(m+n)−1]d−a−[(m−n)−1]d
=2a+2md−2d
=2[a+(m−1)d]
=2t
m
Hence proved
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