If the mth term of a H.P. be n and nth be m, then the rth term will be
Given Tm = n, Tn = m for H.P. therefore for the corresponding A.P. mth term = 1n, nth term = 1m
Let a and d be the first term and common difference of this A.P., then
a+(m−1)d = 1n ......(i)
a+(n−1)d = 1m ......(i)
Solving these, we get a = 1mn, d = 1mn
Now, rth term of corresponding A.P.
= a+(r−1)d = 1mn+(r−1)1mn = 1+r−1mn = rmn
Therefore rth term of corresponding H.P. is mnr
Note : Students should remember this question as a fact.