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KVPY SX SB Exam 2012 Question Paper
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© examsnet.com
Question : 86
Total: 120
Define a sequence
(
a
n
)
by
a
1
=
5
,
a
n
=
a
1
a
2.
.
.
.
a
n
−
1
+
4
for
n
>
1
. Then
lim
n
→
∞
√
a
n
a
n
−
1
equals
1
2
2
5
1
does not exist
Validate
Solution:
a
1
=
5
a
n
=
a
1
a
2
…
.
.
a
n
−
1
+
4
a
2
=
a
1
+
4
=
9
a
3
=
a
1
.
a
2
+
4
=
5
×
9
+
4
=
49
a
4
=
a
1
a
2
a
3
+
4
=
2209
a
5
=
a
1
a
2
a
3
a
4
+
4
=
4870849
=
(
2207
)
2
a
5
=
(
a
4
−
2
)
2
a
4
=
(
49
−
2
)
2
=
(
a
3
−
2
)
2
a
3
=
(
9
−
2
)
2
=
(
a
2
−
2
)
2
a
n
=
(
a
n
−
1
−
2
)
2
√
a
n
=
a
n
−
1
−
2
√
a
n
a
n
−
1
=
a
n
−
1
−
2
a
n
−
1
=
1
−
lim
n
→
∞
2
a
n
−
1
∵
lim
n
→
∞
a
n
−
1
=
∞
=
1
© examsnet.com
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