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Let a(1),a(2),a(3),….,a(4001) is an A.P....

Let `a_(1),a_(2),a_(3),….,a_(4001)` is an `A.P.` such that `(1)/(a_(1)a_(2))+(1)/(a_(2)a_(3))+...+(1)/(a_(4000)a_(4001))=10`
`a_(2)+a_(400)=50`.
Then `|a_(1)-a_(4001)|` is equal to

A

`20`

B

`30`

C

`40`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `(a_(2)-a_(1))/(a_(1)a_(2))+(a_(3)-a_(2))/(a_(2)a_(3))+...+(a_(4001)-a_(4000))/(a_(4001)a_(4000))=10d`
`:.(1)/(a_(1))-(1)/(a_(4001))=10d`
`:. (4000d)/(a_(1)a_(4001))=10d`
`:.a_(1)a_(4001)=400`
also `a_(1)+a_(4001)=50` ,brgt `implies |a_(1)-a_(4001)|^(2)=2500-1600`
`implies|a_(1)-a_(4001)|=30`
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