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Byju's Answer
Standard X
Mathematics
Sum of N Terms of an AP
The sum of fi...
Question
The sum of first
10
term of an A.P is one third of sum of next
10
term. If first term is
−
5
.. Find the sum of its first
30
terms
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Solution
Given,
a
=
−
5
S
10
=
5
[
−
10
+
9
d
]
S
20
=
10
[
−
10
+
19
d
]
S
10
=
1
3
(
S
20
−
S
10
)
5
[
−
10
+
9
d
]
=
1
3
{
10
[
−
10
+
19
d
]
−
5
[
−
10
+
9
d
]
}
15
[
−
10
+
9
d
]
=
{
10
[
−
10
+
19
d
]
−
5
[
−
10
+
9
d
]
}
−
150
+
135
d
=
{
−
100
+
190
d
+
50
−
45
d
}
−
150
+
135
d
=
−
50
+
145
d
−
100
=
10
d
∴
d
=
−
10
S
30
=
30
2
[
2
(
−
5
)
+
(
30
−
1
)
(
−
10
)
]
=
15
[
−
10
+
29
(
−
10
)
]
=
−
4500
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