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The first four terms of a sequence are g...

The first four terms of a sequence are given by `T_(1)=0, T_(2)=1, T_(3) =1, T_(4) =2. The general terms is given by `T_(n)=Aalpha ^(n -1) +B beta ^(n-1)` where A,B` alpha, beta` are independent of a and A is positive.
The value of `(alpha ^(2) + beta ^(2)+ alpha beta)` is equal to :

A

1

B

2

C

5

D

4

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • The first four terms of a sequence are given by T_(1)=0, T_(2)=1, T_(3) =1, T_(4) =2. The general terms is given by T_(n)=Aalpha ^(n -1) +B beta ^(n-1) where A,B alpha, beta are independent of a and A is positive. The value of 5 (A^(2) + B ^(2) is equal to :

    A
    2
    B
    4
    C
    6
    D
    8

  • The fifth term of the sequence for which t_1=1 , t_2=2 and t_(n+2)=t_n+t_(n-1) is

    A
    5
    B
    10
    C
    6
    D
    8

  • If alpha and beta be the roots of equation x^(2) + 3x + 1 = 0 then the value of ((alpha)/(1 + beta))^(2) + ((beta)/(1 + alpha))^(2) is equal to

    A
    `15`
    B
    `18`
    C
    `21`
    D
    `17`

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