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Question

If a1,a2,...a50are in GP, then(a1-a3+a5-...+a49)/(a2-a4+a6-...+a50)is equal to


A

a2/a5

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B

a4/a6

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C

a1/a2

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D

a6/a1

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Solution

The correct option is C

a1/a2


Finding the value of (a1-a3+a5-...+a49)/(a2-a4+a6-...+a50):

Given that a1,a2,...a50 are in GP

Let a be the first time and r be the common ratio

a1=aa2=ara3=ar2an=arn-1(a1-a3+a5-...+a49)/(a2-a4+a6-...+a50)=(a-ar2+ar4+...ar48)/(ar-ar3+ar5+...ar49)=(a-ar2+ar4+...ar48)/r(a-ar2+ar4+....ar48)=1/r=a/ar=a1/a2

Hence, Option (C) is correct.


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