Let an be the nth term of a G.P of positive numbers
100
100
100 Σ
aan
= a and
Σ
a2n-1 = B then the common ratio
n=1
n=1
is
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Answer:
Let a be the first term and r be the common ratio of the G.P.
Then,
n=1
∑
100
a
2n
=α and
n=1
∑
100
a
2n−1
=β
⇒a
2
+a
4
+...+a
200
=α and a
1
+a
3
+...+a
199
=β
⇒ar+ar
3
+...+ar
199
=α and a+ar
2
+...+ar
198
=β
⇒ar{
1−r
2
1−(r
2
)
100
}=α and a{
1−r
2
1−(r
2
)
100
}=β
⇒ar(
1−r
2
1−r
200
)=α, and a(
1−r
2
1−r
200
)=β
⇒r=
β
α
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