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KEAM 2023 Math Solved Paper
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© examsnet.com
Question : 7
Total: 120
Let
a
1
,
a
2
,
a
3
,
.
.
.
be an increasing sequence of natural numbers, which are in an arithmetic progression with common difference
d
. Suppose
a
1
+
a
2
+
a
3
=
27
and
a
1
2
+
a
2
2
+
a
3
2
=
275
. Then the values of
a
1
,
d
are
a
1
=
3
;
d
=
2
a
1
=
−
5
;
d
=
4
a
1
=
4
;
d
=
5
a
1
=
−
4
;
d
=
5
(F)
a
1
=
5
;
d
=
4
Validate
Solution:
a
1
=
a
a
2
=
a
+
d
a
3
=
a
+
2
d
3
a
+
3
d
=
27
(given)
a
+
d
=
9
a
1
2
+
a
2
2
+
a
3
2
=
3
a
2
+
6
a
d
+
5
d
2
275
=
3
[
a
2
+
2
a
d
+
d
2
]
+
2
d
2
=
3
(
a
+
d
)
2
+
2
d
2
275
=
3
(
81
)
+
2
d
2
d
2
=
275
−
243
2
=
16
∴
a
+
d
=
a
+
4
=
9
⇒
a
=
5
a
=
5
,
d
=
4
© examsnet.com
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