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CMAT 2015 Solved Question Paper
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© examsnet.com
Question : 2
Total: 100
If each term of GP is positive and is the sum of the two preceding terms, then the common ratio of GP is
(
√
5
−
1
)
2
(
1
−
√
5
)
2
(
√
5
+
1
)
2
(
√
3
+
1
)
2
Validate
Solution:
(c) Let the first term be a and common ratio be r, then GP
series will be a, ar, a
r
2
,
ar
3
,...
According to the question,
a
r
2
= a + ar
⇒ a
r
2
= a(1 + r) ⇒
r
2
- r - 1 = 0
⇒ r =
1
±
√
(
−
1
)
2
−
4
(
1
)
(
−
1
)
2
×
1
[
∵
x
=
−
b
±
√
b
2
−
4
a
c
2
a
]
=
1
±
√
1
+
4
2
×
1
=
1
±
√
5
2
Since, terms are positive
So, r = ( 1 +
√
5
)/2
© examsnet.com
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