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Question

Let an be the the nth term of a G.P. of positive numbers such that 100n=1a2n=α and 100n=1a2n1=β, αβ. Then the common ratio of G.P. is

A
αβ
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B
βα
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C
αβ
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D
βα
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Solution

The correct option is A αβ
Let first term and common ratio of G.P. be a and r respectively.
100n=1a2n=α
a2+a4+a6++a200=α
ar+ar3+ar5++ar199=α
ar(1+r2+r4++r198)=α (1)

100n=1a2n1=β
a1+a3+a5++a199=β
a+ar2++ar198=β
a(1+r2++r198)=β (2)
Dividing (1) and (2), we get
r=αβ

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