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Mathematics
Mathematics
Problem
Identify the correct sigma notation for the sum of the first
n
n
n
terms of an arithmetic progression with first term
a
a
a
and common difference
d
d
d
. a)
∑
k
=
0
n
[
a
+
k
d
]
\displaystyle\sum_{k=0}^{n}[a+kd]
k
=
0
∑
n
[
a
+
k
d
]
b)
∑
k
=
1
n
[
a
+
k
d
]
\displaystyle\sum_{k=1}^{n}[a+kd]
k
=
1
∑
n
[
a
+
k
d
]
c)
∑
k
=
1
n
[
a
+
(
k
−
1
)
d
]
\displaystyle\sum_{k=1}^{n}[a+(k-1)d]
k
=
1
∑
n
[
a
+
(
k
−
1
)
d
]
d)
1
2
∑
k
=
1
n
[
2
a
+
(
k
−
1
)
d
]
\displaystyle\dfrac{1}{2}\sum_{k=1}^{n}[2a+(k-1)d]
2
1
k
=
1
∑
n
[
2
a
+
(
k
−
1
)
d
]
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