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Let alpha,beta be the roots of x^2-x-1=0...

Let `alpha,beta` be the roots of `x^2-x-1=0` and `S_n=alpha^n+beta^n`, for all integers `nge1`. Then for every integer `nge2`,

A

S_n+S_(n+1)=S_(n+1)`

B

S_n-S_(n-1)=S_(n+1)`

C

`S_(n-1)=S_(n+1)`

D

S_n+S_(n-1)=2S_(n+1)`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • Let alpha,beta be the roots of x^(2)-x-1=0ands_(n)=alpha^(n)+beta^(n) for all integers nge1 . Then for every integer nge2 -

    A
    `S_(n)+S_(n-1)=S_(n+1)`
    B
    `S_(n)+S_(n-1)=S_(n)`
    C
    `S_(n-1)=S_(n+1)`
    D
    `S_(n)+S_(n-1)=2S_(n+1)`

  • Let alpha and beta be the roots of the equation x^2-6x-2=0 . If a_n=alpha^n-beta^n , for nge1 , then the value of (a_10-2a_8)/(2a_9) is equal to

    A
    -6
    B
    3
    C
    -3
    D
    6

  • Let alpha and beta be the roots of equation x^(2)-6x-2=0." If " a_(n)=alpha^(n)-beta^(n)," for "nge1 , "then the value of " ((a_(10))-(2a_(8)))/(2a_(9)) is equal to -

    A
    3
    B
    `-3`
    C
    6
    D
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