if sum of first 10 terms of an A.P is equal to the sum of next 10 terms of same A.P. If a=3 then find its 23rd term.
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Answer:
Given,
S
10
=
−
150
S
20
−
S
10
=
Next 10 term
S
20
−
S
10
=
−
550
S
20
=
−
550
+
S
10
S
20
=
−
550
−
150
S
20
=
−
700
S
n
=
n
2
[
2
a
+
(
n
−
1
)
d
]
S
10
=
10
2
[
2
a
+
(
10
−
1
)
d
]
=
−
150
2
a
+
9
d
=
−
30
(i)
S
20
=
−
700
20
2
[
2
a
+
19
d
]
=
−
700
2
a
+
19
d
=
−
70
(ii)
eq(i)-eq(ii)
(
2
a
+
9
d
=
−
30
)
−
(
2
a
+
19
d
=
−
70
)
−
10
d
=
40
d
=
−
4
2
a
+
9
d
=
−
30
2
a
=
−
30
+
36
⇒
a
=
3
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