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Math Help - geometric sequence

  1. #1
    Senior Member polymerase's Avatar
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    Exclamation geometric sequence

    Find a, r, and Tn for each geometric sequence
    a)t4=24 and t6=96 b)t2=-6 and t5=-162
    -thank you for whoever answers my question .......
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by polymerase View Post
    Find a, r, and Tn for each geometric sequence
    a)t4=24 and t6=96
    a) t_4 =24 and t_6 = 96

    In general
    t_n = t_1 \cdot r^{n - 1}

    We have
    t_4 = t_1 \cdot r^3 = 24
    t_6 = t_1 \cdot r^5 = 96

    Thus
    \frac{t_6}{t_4} = \frac{96}{24} = r^2

    or

    r^2 = 4

    Thus r = \pm 2

    Take r = 2:
    t_4 = 24 = t_1 \cdot (2)^3 = 8t_1

    Thus t_1 = 3 and t_n = 3(2)^{n - 1}

    Take r = -2:
    t_4 = 24 = t_1 \cdot (-2)^3 = -8t_1

    Thus t_1 = -3 and t_n = -3(-2)^{n - 1}

    Both series will produce the correct terms.

    -Dan
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by polymerase View Post
    Find a, r, and Tn for each geometric sequence
    b)t2=-6 and t5=-162
    Follow the same steps as before.
    t_n = t_1 \cdot r^{n - 1}

    with
    t_2 = -6 = t_1 \cdot r
    t_5 = -162 = t_1 \cdot r^4

    Dividing I get that
    r = 3

    and from there I get that
    t_1 = -2

    Thus
    t_n = -2(3)^{n - 1}

    -Dan
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