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EAMCET Engineering 2009 Solved Paper
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© examsnet.com
Question : 83
Total: 160
Using mathematical induction, the numbers
a
n
's are defined by,
a
0
=
1
,
a
n
+
1
=
3
n
2
+
n
+
a
n
,
(
n
≥
0
)
.
Then,
a
n
is equal to
n
3
+
n
2
+
1
n
3
−
n
2
+
1
n
3
−
n
2
n
3
+
n
2
Validate
Solution:
Given,
a
0
=
1
,
a
n
+
1
=
3
n
2
+
n
+
a
n
⇒
a
1
=
3
(
0
)
+
0
+
a
0
=
1
and
a
2
=
3
(
1
)
2
+
1
+
a
1
=
3
+
1
+
1
=
5
From option (b),
Let
P
(
n
)
=
n
3
−
n
2
+
1
∴
P
(
0
)
=
0
−
0
+
1
=
1
=
a
0
P
(
1
)
=
1
3
−
1
2
+
1
=
1
=
a
1
and
P
(
2
)
=
(
2
)
3
−
(
2
)
2
+
1
=
5
=
a
2
Hence, option (b) is correct.
© examsnet.com
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