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Byju's Answer
Standard XII
Mathematics
Implicit Differentiation
If mth term...
Question
If
m
t
h
term of HP is n while
n
t
h
term is m find its
(
m
+
n
)
t
h
term
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Solution
Given
T
m
=
n
o
r
1
a
+
(
m
−
1
)
d
=
n
where a is the first term and d is the common difference of the corresponding AP
So
a
+
(
m
−
1
)
d
=
1
n
and
a
+
(
n
−
1
)
d
=
1
m
⇒
(
m
−
n
)
d
=
m
−
n
m
n
d
=
1
m
n
So
a
=
1
n
−
(
m
−
1
)
m
n
=
1
m
n
Hence
T
(
m
+
n
)
=
1
a
+
(
m
+
n
−
1
)
d
=
m
n
1
+
m
+
n
−
1
=
m
n
m
+
n
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