Question

If m term of HP is n and nth term is m,then find m+n th term.

Answer 1

we have,
mth term = n
=> a+(m-1)d = n --- (1)

nth term = m
=> a+(n-1)d = m --- (2)

subtracting (1) from (2), we get,
(n-1)d-(m-1)d = m-n
=> dn-d-dm+d = m-n
=> d(n-m) = m-n
=> d = (m-n)/-(m-n)
=> d = -1

putting d = -1 in (1)
a+(m-1)(-1) = n
=> a-m+1 = n
=> a = m+n-1

now,
(m+n) th term = a+(m+n-1)d
= m+n-1+(m+n-1)(-1)
= m+n-1-m-n+1
= 0
hence (m+n) th term of the AP is 0