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Test Index
JEE Main Math Class 11 Sequences and Series Part 1 Questions
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© examsnet.com
Question : 5
Total: 100
The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is
27
19
. Then the common ratio of this series is :
[Jan. 11, 2019 (I)]
1
3
2
3
2
9
4
9
Validate
Solution:
Let the terms of infinite series are
a
,
a
r
,
a
r
2
,
a
r
3
,
.
.
.
So,
a
1
−
r
=
3
Since, sum of cubes of its terms is
27
19
that is sum of
a
3
,
a
3
r
3
,
.
.
.
∞
is
27
19
So,
a
3
1
−
r
3
=
27
19
⇒
a
1
−
r
×
a
2
(
1
+
r
2
+
r
)
=
27
19
⇒
9
(
1
+
r
2
−
2
r
)
×
3
1
+
r
2
+
r
=
27
19
⇒
6
r
2
−
13
r
+
6
=
0
⇒
(
3
r
−
2
)
(
2
r
−
3
)
=
0
⇒
r
=
2
3
,
or
3
2
As
|
r
|
<
1
So,
r
=
2
3
© examsnet.com
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