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Mathematics
Mathematics
Problem
Which of the following is the correct expression for the sum
S
n
S_n
S
n
of the first
n
n
n
terms of an arithmetic progression whose first term is
a
a
a
and common difference is
d
d
d
? a)
S
n
=
n
2
[
a
+
(
n
−
1
)
d
]
\displaystyle S_n = \frac{n}{2}\bigl[a + (n-1)d\bigr]
S
n
=
2
n
[
a
+
(
n
−
1
)
d
]
b)
S
n
=
n
2
[
2
a
+
n
d
]
\displaystyle S_n = \frac{n}{2}\bigl[2a + nd\bigr]
S
n
=
2
n
[
2
a
+
n
d
]
c)
S
n
=
n
2
[
2
a
+
(
n
−
1
)
d
]
\displaystyle S_n = \frac{n}{2}\bigl[2a + (n-1)d\bigr]
S
n
=
2
n
[
2
a
+
(
n
−
1
)
d
]
d)
S
n
=
n
[
a
+
(
n
−
1
)
d
]
\displaystyle S_n = n\bigl[a + (n-1)d\bigr]
S
n
=
n
[
a
+
(
n
−
1
)
d
]
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