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Math Help - Geometric sequence & series

  1. #1
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    Geometric sequence & series

    A sequence of numbers u_1, u_2, , u_n, is given by the formula u_n = 3(\frac{2}{3})^n - 1 where n is a positive integer.
    (a) Find the value of u_1, u_2 and u_3.
    (b) Show that \sum_{n=1}^{15} u_n = -9.014 to 4 s.f.
    (c) Proved that u_{n+1} = 2 (\frac{2}{3})^3 - 1.
    ------------------------

    (a) u_1 = 1, u_2 = 1/3 & u_3 = -1/9.

    How could I do rest of them?
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by geton View Post
    A sequence of numbers u_1, u_2, , u_n, is given by the formula u_n = 3(\frac{2}{3})^n - 1 where n is a positive integer.
    (a) Find the value of u_1, u_2 and u_3.
    (b) Show that \sum_{n=1}^{15} u_n = -9.014 to 4 s.f.
    (c) Proved that u_{n+1} = 2 (\frac{2}{3})^3 - 1.
    ------------------------

    (a) u_1 = 1, u_2 = 1/3 & u_3 = -1/9.

    How could I do rest of them?
    The sum of n terms in a geometric series

    S_n= (a+k)+(at+k)+(at^2+k)+(at^3+k)....+(at^n+k)

    ie; series with first term a and common factor t is
     <br /> <br />
S_n =\frac{a(t^n-1)}{t-1} + (n+1)k <br /> <br />

    you have  <br /> <br />
a= u_1 = 1 <br /> <br />
     <br /> <br />
t=\frac{2}{3}<br /> <br />

    k= (-1) and n =15

    put them in the formula

    about 3rd question I think its incorrect
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