Question

10.
If mth term of a H.P. is n and nth term is m, then (m + n)th term is
a)0 b)1 c)-1 d)mn/m+n​

Answer 1

Given that,m
th
term of an H.P. is n and n
th
term is m.

Therefore, m
th
term of an A.P. is
n
1
​
and n
th
term is
m
1
​
.

Let, a be the first term and d be the common difference of the A.P

Now, t
m
​
=a+(m−1)d=
n
1
​
....(1)

And t
n
​
=a+(n−1)d=
m
1
​
....(2)

Subtracting (1) & (2), we get

(m−n)d=
n
1
​
−
m
1
​


⇒d=
mn
1
​


Substituting d in (1), we get

a+
mn
(m−1)
​
=
n
1
​
⇒a=
mn
1
​


Therefore, t
mn
​
=a+(mn−1)d=
mn
1
​
+
mn
(mn−1)
​
=1

and thus mn
th
term of H.P is 1.