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JEE Main Math Class 11 Sequences and Series Part 1 Questions
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© examsnet.com
Question : 26
Total: 100
Let
A
be the sum of the first 20 terms and
B
be the sum of the first 40 terms of the series
1
2
+
2
⋅
2
2
+
3
2
+
2
⋅
4
2
+
5
2
+
2
⋅
6
2
+
.
.
.
If
B
−
2
A
=
100
λ
,
then
λ
is equal to
[2018]
248
464
496
232
Validate
Solution:
Here,
B
−
2
A
=
40
∑
n
=
1
a
n
−
2
20
∑
n
=
1
a
n
=
40
∑
n
=
21
a
n
−
2
20
∑
n
=
1
a
n
B
−
2
A
=
(
21
2
+
2.22
2
+
23
2
+
2.24
2
+
.
.
.
.
.
+
40
2
)
−
(
1
2
+
2.2
2
+
3
2
+
2.4
2
.
.
.
.
.
+
20
2
)
=
20
[
22
+
2.24
+
26
+
2.28
+
.
.
.
.
.
+
60
]
=
20
[
⏟
(
22
+
24
+
26
.
.
.
60
)
20
terms
+
⏟
(
24
+
28
+
.
.
.
.
+
60
)
10
terms
]
20
[
20
2
(
22
+
60
)
+
10
2
(
24
+
60
)
]
=
10
[
20.82
+
10.84
]
=
100
[
164
+
84
]
=
100.248
© examsnet.com
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