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Let a(1),a(2),…, a(10) be a G.P.. If (a(...

Let `a_(1),a_(2),…, a_(10)` be a G.P.. If `(a_(3))/(a_(1))` = 25, then `(a_(9))/(a_(5))` equals

A

`5^(3)`

B

`2(5^(2))`

C

`4(5^(2))`

D

`5^(4)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let r be the common ratio of given GP, then we have the following sequence `a_(1), a_(2) = a_(1) r, a_(3) = a_(1) r^(2), ..., a_(10) = a_(1) r^(9)`
Now, `a_(3) = 25 a_(1)`
`rArr a_(1) r^(2) = 25 a_(1)` ltbr. `rArr r^(2) = 25`
Consider, `(a_(9))/(a_(5)) = (a_(1) r^(8))/(a_(1) r^(4)) = r^(4) = (25)^(2) = 5^(4)`
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