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AP EAMCET Engineering 21 Sep 2020 Shift 2 Paper
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© examsnet.com
Question : 18
Total: 160
The sum of the cubes of three consecutive natural numbers is divisible by
26
25
9
7
Validate
Solution:
(c) Let the three consecutive natural numbers
(
n
−
1
)
,
n
,
n
+
1
where
n
≥
2
∴ Sum of cubes of the three consecutive natural numbers is
(
n
−
1
)
3
+
n
3
+
(
n
+
1
)
3
=
3
n
3
+
6
n
=
3
n
(
n
2
+
2
)
For each value of
n
≥
2
, the expression
3
n
(
n
2
+
2
)
is divisible by 9.
© examsnet.com
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