Show that the sum of `(m+n)^(t h)a n d\ (m-n)^(t h)` term of an A.P. is equal to twice the `m^(t h)` term.

Explanation

Let a and d be the first term and the common difference of A.P. respectively.

It is known that the `k^(th)` term of an A.P. is given by

`a_k` `=a+(k−1)d`

∴`a _(m+n)``=a+(m+n−1)d`

`a_(m−n)``​=a+(m−n−1)d`

`a_m` `=a+(m−1)d`

∴`a _(m+n)` +`a _(m−n)` `=a+(m+n−1)d+a+(m−n−1)d`

`=2a+(m+n−1+m−n−1)d`
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