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JEE Main Math Class 11 Sequences and Series Part 1 Questions
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© examsnet.com
Question : 2
Total: 100
The product of three consecutive terms of a G.P. is 512 . If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is :
[Jan. 12, 2019 (I)]
36
32
24
28
Validate
Solution:
Let three terms of a G.P. be
a
r
,
a
,
a
r
a
r
⋅
a
⋅
a
r
=
512
a
3
=
512
⇒
a
=
8
4 is added to each of the first and the second of three terms then three terms are,
8
r
+
4
,
8
+
4
,
8
r
.
∵
8
r
+
4
,
12
,
8
r
form an A.P.
∴
2
×
12
=
8
r
+
8
r
+
4
⇒
2
r
2
−
5
r
+
2
=
0
⇒
(
2
r
−
1
)
(
r
−
2
)
=
0
⇒
r
=
1
2
or 2
Therefore, sum of three terms
=
8
2
+
8
+
16
=
28
© examsnet.com
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