Every term an HP is the reciprocal of the corresponding terms of an AP. Let a be the first term and d be the common difference of the AP. According to the question: Tm=n ⇒
1
a+(m−1)d
=n ⇒a+(m−1)d=
1
n
..... (1) Tn=m ⇒
1
a+(n−1)d
=m ⇒a+(n−1)d=
1
m
....... (2) Subtracting equation (2) from equation (1), we get : (m−n)d=
1
n
−
1
m
⇒d=
1
mn
.....(3) Substituting this value of d in any of the equations (1) or (2), we get: ⇒a+(m−1)(
1
mn
)=
1
n
⇒a=
1
n
−
m−1
mn
⇒a=
1
mn
.......(4) The (m+n)th term of the AP will be: am+n=a+(m+n−1)d Using the values in equations (3) and (4), we get: ⇒am+n=