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Question
Mathematics
An A.P. consists of n (odd terms) and its middle term is m. Then the sum of the A.P. is
Q. An A.P. consists of n (odd terms) and its middle term is m. Then the sum of the A.P. is
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196
Sequences and Series
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A
2 mn
8%
B
1/2 mn
15%
C
mn
67%
D
m
n
2
.
10%
Solution:
Middle term
2
T
n
+
1
=
a
+
(
2
n
+
1
−
1
)
d
=
m
⇒
2
a
+
(
n
+
1
−
2
)
d
=
2
m
⇒
2
a
+
(
n
−
1
)
d
=
2
m
⇒
2
n
[
2
a
+
(
n
−
1
)
d
]
=
2
n
(
2
m
)
=
mn
⇒
S
n
of
A
.
P
.
=
mn