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The sequence {x(1),x(2),…x(50)} has the ...

The sequence `{x_(1),x_(2),…x_(50)}` has the property that for each `k`, `x_(k)` is `k` less than the sum of other `49` numbers. The value of `96x_(20)` is

A

`300`

B

`315`

C

`1024`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` We have `x_(k)+k=S-x_(k)` where `x_(1)+x_(2)+…+x_(k)=S`
`implies2x_(k)+k=S`
`:.2sum_(k=1)^(50)x_(k)+sum_(k=1)^(50)k=sum_(k=1)^(50)S` ,brgt `implies2(S)+(50.51)/(2)=50S`
`implies48(S)=25.51`
`impliesx_(20)=((25.51)/(48)-20)(1)/(2)=(315)/(96)`
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