In an A.P., if mth term is n and nth term is m, show that its rth term is ( m+n-r)

Home Work Help
,
1

In an A.P., if mth term is n and nth term is m, show that its rth term is ( m+n-r)

2

AP
we have
am = a + (m - 1)d = n…(1)
an = a + (n - 1)d = m…(2)
from (1) and (2) we have
(m -n)d =n - m
d = - 1. . . . . . ( 3)
and a = n + m - 1
Now for rth term we have
ar = a + (r - 1)d
= n + m - 1+ (r - 1) ( -1)
= n + m - r
Hence rth term will be n + m - r