Question

In an A. P., if $m^{th}$ is n and $n^{th}$ term is m, show that its $r^{th}$ term is (m +n -r).

Answer 1

$m^{th}$ term = a + (m-1)d = n .......(1)

$n^{th}$ term = a + (n - 1)d = m...............(2)

on solving 1 and 2

a = n + m - 1

d = -1

$r^{th}$ term = a + (r - 1)d = n + m - 1 + (r - 1)$\times$(-1) = n + m -r

Hence proved