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Byju's Answer
Standard XII
Mathematics
Arithmetic Progression
Find the sum ...
Question
Find the sum of first
10
terms of following series
S
=
3
(
1
)
1
+
5
(
1
3
+
2
3
)
1
2
+
2
2
+
7
(
1
3
+
2
3
+
3
3
)
1
2
+
2
2
+
3
2
+
.
.
.
.
A
440
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B
450
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C
660
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D
220
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Solution
The correct option is
C
660
First we shall find the
r
th
term of the given series
T
r
=
(
2
r
+
1
)
[
r
(
r
+
1
)
2
]
2
r
(
r
+
1
)
(
2
r
+
1
)
6
=
3
r
(
r
+
1
)
2
T
r
=
3
2
[
r
2
+
r
]
S
n
=
∑
T
r
=
3
2
[
n
(
n
+
1
)
(
2
n
+
1
)
6
+
n
(
n
+
1
)
2
]
S
10
=
3
2
[
10
×
11
×
21
6
+
10
×
11
2
]
S
10
=
3
2
[
385
+
55
]
=
660
Suggest Corrections
0
Similar questions
Q.
Find the sum of first
10
terms of following series
S
=
3
(
1
)
1
+
5
(
1
3
+
2
3
)
1
2
+
2
2
+
7
(
1
3
+
2
3
+
3
3
)
1
2
+
2
2
+
3
2
+
.
.
.
.
Q.
Let
S
=
3
+
5
(
1
3
+
2
3
)
1
2
+
2
3
+
7
(
1
3
+
2
3
+
3
3
1
2
+
2
2
+
3
2
+
.
.
.
Then the sum up to 10 terms is
Q.
The value of
3
×
1
3
1
2
+
5
×
(
1
3
+
2
3
)
1
2
+
2
2
+
7
×
(
1
3
+
2
3
+
3
3
)
1
2
+
2
2
+
3
2
+
⋯
upto
10
terms
, is
Q.
The sum
3
×
1
3
1
2
+
5
×
(
1
3
+
2
3
)
1
2
+
2
2
+
7
×
(
1
3
+
2
3
+
3
3
)
1
2
+
2
2
+
3
2
+
⋯
upto
10
th
term, is :
Q.
Find the sum of first
n
terms of the series
1
2
+
(
1
2
+
2
2
)
+
(
1
2
+
2
2
+
3
2
)
+
.
.
.
.
.
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