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AIEEE 2002 Math Solved Paper
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© examsnet.com
Question : 26
Total: 74
Sum of infinite number of terms of GP is 20 and sum of their square is 100 . The common ratio of GP is
5
3
5
8
5
1
5
Validate
Solution:
Let
a
=
first team of
G
.
P
. and
r
=
common ratio of
G
.
P
; ;
Then G.P. is
a
,
a
r
,
a
r
2
Given
S
∞
=
20
⇒
a
1
−
r
=
20
⇒
a
=
20
(
1
−
r
)
]
............(i)
Also
a
2
+
a
2
r
2
+
a
2
r
4
+
.
.
.
to
∞
=
100
⇒
a
2
1
−
r
2
=
100
⇒
a
2
=
100
(
1
−
r
)
(
1
+
r
)
....(ii)
From
(
i
)
,
a
2
=
400
(
1
−
r
)
2
From
(
i
i
)
, we get
100
(
1
−
r
)
(
1
+
r
)
=
400
(
1
−
r
)
2
⇒
1
+
r
=
4
−
4
r
⇒
5
r
=
3
⇒
r
=
3
∕
5
© examsnet.com
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