Question

If the m^th term of an HP is n and nth is m, then the r^th term will be

(a)  r/mn

(b)  mn/r + 1

(c)  mn/r

(d)  mn/r - 1

Answer 1

Correct option  (c) mn/r

Given T_m = n,T_n = m for HP. Therefore,for the corresponding AP m^th term = 1/n,n^th term = 1/m.

Let a and d be the first term and common difference of this AP. Then  a  + (m - 1)d = 1/n  ...(1)

a + (n - 1)d = 1/m   ......(2)

Solving these, we get a = 1/mn, d = 1/mn

Now, r th term of corresponding AP is 

Therefore, r^th term of corresponding HP is  mn/r.