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Let a(n)=[log((7)/(5))]^(n) and b(n) =lo...

Let `a_(n)=[log((7)/(5))]^(n) and b_(n) =log_(5) (a_(n)) AA n in N`. Then `b_(1),b_(2),b_(3),…` are in

A

A.P

B

G.P

C

H.P

D

A.G.P

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Knowledge Check

  • If lta_(n)gtandltb_(n)gt be two sequences given by a_(n)=(x)^((1)/(2^(n)))+(y)^((1)/(2^(n))) and b_(n)=(x)^((1)/(2^(n))) -(y)^((1)/(2^n)) for all ninN . Then, a_(1)a_(2)a_(3) . . . . .a_(n) is equal to

    A
    x-y
    B
    `(x+y)/(b_(n))`
    C
    `(x-y)/(b_(n))`
    D
    `(xy)/(b_(n))`

  • We know that , if a_(1),a_(2),….a_(n) are in A.P and vice versa . If a_(1),a_(2),…a_(n) are in A.P and vice versa . If a_(1),a_(2)….a_(n) are in A.P with common difference d, then for nay (b gt 0) the numbers b^(a_(1)),b^(a_(2)),b^(a_(3)),....,b^(a_(n)) are in G.P with common ratio b^(d) If a_(1),a_(2),.....a_(n) are positive and in G.P with common ratio r , then for any base b(b gt 0), log_(b) a_(1) , log _(b) a_(2) , ..., log_(b) a_(n) are in A.P with common difference log_(b)r If a,b,c,d are in G.P and a^(x) = b^(y) = c^(z) = d^(v) , then x, y , z , v are in

    A
    A.P
    B
    G.P
    C
    H.P
    D
    None of these

  • Let a_(n)=3^(n)+5^(n), nin N and let A=((a_(n),a_(n+1),a_(n+2)),(a_(n+1),a_(n+2),a_(n+3)),(a_(n+2),a_(n+3),a_(n+4))) Then

    A
    0 is a root of the equation det (A-xl) =0
    B
    det (A) =`a_(n)a_(n+2) a_(n+4)`
    C
    det (A) `lt0`
    D
    det (A) `= a_(n)+a_(n+2)+a_(n+4)`

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