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Question

In a H.P. pth term is q and qth term is p. Then the (pq)th term is

A
Zero
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B
p+qpq
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C
1
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D
pqp+q
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Solution

The correct option is C 1
Solution:
Given that: tp=q,tq=p
To find: tpq=?
Solution:
Let, a be first term and d be common difference of an A.P.
tp=q1a+(p1)d=qa+(p1)d=1q............(i) and
tq=p1a+(q1)d=pa+(q1)d=1p.................(ii)
Subtracting eqs. (ii) from (i), we get
(pq)d=1q1p(pq)d=pqpq
or, d=1pq
Putting value of d in eqn(i), we get
a=1pq
Now,
tpq=1a+(pq1)d=11pq+(pq1)1pq=pq1+pq1=pqpq=1
Hence, C is the correct option.

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