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If a(1),a(2),a(3),… are in G.P., where a...

If `a_(1),a_(2),a_(3),…` are in `G.P.`, where `a_(i) in C` (where `C` satands for set of complex numbers) having `r` as common ratio such that `sum_(k=1)^(n)a_(2k-1)sum_(k=1)^(n)a_(2k+3) ne 0` , then the number of possible values of `r` is

A

`2`

B

`3`

C

`4`

D

`5`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` We have `a_(1)+a_(3)+a_(5)+….+a_(2n-1)`
`=a_(5)+a_(7)+a_(9)+…+a_(2n-3)`
`=r^(4)(a_(1)+a_(3)+…+a_(2n-1))`
`impliesr^(4)=1`
`impliesr=1,-1,i` and `-i`.
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