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

Answer

N/a

Explanation

Let the first term be 'a' and common difference be d of the A.P.
`therefore` `T_(m + n) + T_(m - n)`
`= a + (m + n -1) d + a + (m - n - 1) d`
`= 2a + (2m - 2) d`
`= 2 [a + (m - 1) d]`
`= 2 * T_(m)" "` Hence Proved.