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Mathematics
Problem
For an arithmetic progression with first term
a
a
a
and common difference
d
d
d
, let
T
n
=
a
1
+
a
3
+
a
5
+
⋯
+
a
2
n
−
1
T_n=a_1+a_3+a_5+\dots+a_{2n-1}
T
n
=
a
1
+
a
3
+
a
5
+
⋯
+
a
2
n
−
1
be the sum of the first
n
n
n
odd-indexed terms. Which expression represents
T
n
T_n
T
n
? a)
n
[
a
+
2
(
n
−
1
)
d
]
n\,[a+2(n-1)d]
n
[
a
+
2
(
n
−
1
)
d
]
b)
n
2
[
2
a
+
(
n
−
1
)
d
]
\dfrac{n}{2}\,[2a+(n-1)d]
2
n
[
2
a
+
(
n
−
1
)
d
]
c)
n
[
a
+
(
n
−
1
)
d
]
n\,[a+(n-1)d]
n
[
a
+
(
n
−
1
)
d
]
d)
n
[
a
+
(
2
n
−
1
)
d
]
n\,[a+(2n-1)d]
n
[
a
+
(
2
n
−
1
)
d
]
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