In a harmonic progression pth term is q and the qth term is p. Then the pqth term is
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Step-by-step explanation:
Solution:
Given that: t
p
=q,t
q
=p
To find: t
pq
=?
Answer----Let, a be first term and d is common difference of an A.P.
t
p
=q⟹
a+(p−1)d
1
=q⟹a+(p−1)d=
q
1
............(i) and
t
q
=p⟹
a+(q−1)d
1
=p⟹a+(q−1)d=
p
1
.................(ii)
Subtracting equn (ii) from (i), we get
(p−q)d=
q
1
−
p
1
⟹(p−q)d=
pq
p−q
or, d=
pq
1
Putting value of d in eqn(i), we get
a=
pq
1
Now,
t
pq
=
a+(pq−1)d
1
=
pq
1
+(pq−1)
pq
1
1
=
1+pq−1
pq
=
pq
pq
=1
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