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Byju's Answer
Standard X
Mathematics
General Term of an AP
If the sum of...
Question
If the sum of first
7
terms of an AP is
49
and that of
17
terms is
289
, find the sum of first
n
terms.
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Solution
Given
S
7
=
49
and
S
17
=
289
By using
S
n
=
n
2
[
2
a
+
(
n
−
1
)
d
]
we have,
S
7
=
7
2
[
2
a
+
(
7
−
1
)
d
]
=
49
⇒
49
=
7
2
[
2
a
+
(
7
−
1
)
d
]
⇒
49
=
7
2
(
2
a
+
6
d
)
⇒
7
=
a
+
3
d
⇒
a
+
3
d
=
7
...................(i)
S
17
=
17
2
[
2
a
+
(
17
−
1
)
d
]
=
289
⇒
289
=
17
2
[
2
a
+
(
17
−
1
)
d
]
⇒
289
=
17
2
(
2
a
+
16
d
)
⇒
17
=
a
+
8
d
⇒
a
+
8
d
=
17
......................(ii)
Substituting (i) from (ii), we get
5
d
=
10
or
d
=
2
From equation (i),
a
+
3
(
2
)
=
7
a
+
6
=
7
or
a
=
1
S
n
=
n
2
[
2
(
1
)
+
(
n
−
1
)
2
]
=
n
2
[
2
+
(
n
−
1
)
2
]
=
n
2
(
2
+
2
n
−
2
)
=
n
2
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