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Given the sequence of numbers x(1),x(2),...

Given the sequence of numbers `x_(1),x_(2),x_(3),x_(4),….,x_(2005)`, `(x_(1))/(x_(1)+1)=(x_(2))/(x_(2)+3)=(x_(3))/(x_(3)+5)=...=(x_(2005))/(x_(2005)+4009)`, the nature of the sequence is

A

`A.P.`

B

`G.P.`

C

`H.P.`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` Given `(x_(1))/(x_(1)+1)=(x_(2))/(x_(2)+3)=(x_(3))/(x_(3)+5)=...=(x_(2005))/(x_(2005)+4009)`
`impliesx_(1)=(lambda)/(1-lambda)`, `x_(2)=(3lambda)/(1-lambda)`, `x_(3)=(5lambda)/(1-lambda)`,……
Hence , `x_(1),x_(2),x_(3),…..,x_(2005)` are in arithmetic progression.
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