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the first term of geometric sequence is 24 and the third term is 6, find the fourth term and expression for the nth term.?

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  • 8 months ago

    The first term of geometric sequence is 24 and the third term is 6.

    The fourth term is 3.

    24, 12, 6, 3, ...

    The expression for the n th term:

    an = 3 × 2^(4 - n)

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  • Como
    Lv 7
    8 months ago

    a = 24 , a r² = 6

    r² = 6/24 = 1/4

    r = 1/2

    Terms are 24 , 12 , 6 , 3

    Un = 24 x (1/2)^(n - 1)

    Un = 48 / 2^n

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  • 8 months ago

    24k^2 = 6

    k = { -1/2 , 1/2}

    Fourth term = { 3 , -3 }

    X_n = 48(.5)^n ; 48(-.5)^n

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  • 8 months ago

    24, 12, 6, 3, ..., 48/(2)ⁿ, ...

    or

    24, -12, 6, -3, ..., -48/(-2)ⁿ, ...

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  • rotchm
    Lv 7
    8 months ago

    You Are given: 24, 24r, 24r², 24r^3, ... You are then told that 24r² = 6. So what is r?

    So what is then 24r^3?

    Then 24rⁿ?

    Done!

    Hopefully no one will spoil you the answer thereby depriving you from your personal enhancement; that would be very inconsiderate of them.

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  • 8 months ago

    t_n = t(n-1) * r

    so

    t_1 = 24

    t_2 = 24 * r

    t_3 = 24*r^2 = 6

    ==> r^2 = 6/24 = 1/4

    ==> r = 1/2

    so t_4 = 3

    and t_n = 24*2^(-n)

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