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Mathematics
If the sum of first 11 terms of an A.P., a1 a2, a3, ldots is 0(a1 ≠ 0), then the sum of the A.P., a 1, a 3, a 5, ldots, a 23 is ka 1, where k is equal to :
Q. If the sum of first
11
terms of an
A
.
P
.
,
a
1
a
2
,
a
3
,
…
is
0
(
a
1
=
0
)
,
then the sum of the
A
.
P
.
,
a
1
,
a
3
,
a
5
,
…
,
a
23
is
k
a
1
,
where
k
is equal to :
2623
215
JEE Main
JEE Main 2020
Sequences and Series
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A
10
121
29%
B
−
5
72
43%
C
5
72
29%
D
−
10
121
0%
Solution:
a
1
+
a
2
+
a
3
+
…
..
+
a
11
=
0
⇒
(
a
1
+
a
11
)
×
2
11
=
0
⇒
a
1
+
a
11
=
0
⇒
a
1
+
a
1
+
10
d
=
0
where
d
is common difference
⇒
a
1
=
−
5
d
a
1
+
a
3
+
a
5
+
……
+
a
23
=
(
a
1
+
a
23
)
×
2
12
=
(
a
1
+
a
1
+
22
d
)
×
6
=
(
2
a
1
+
22
(
5
−
a
1
)
)
×
6
=
−
5
72
a
1
⇒
K
=
5
−
72