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Math Help - geometric sequences (please help)

  1. #1
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    geometric sequences (please help)

    sequence 40, -20, 10. -5... is geometric
    find Un and hence find the 10th term

    what i got was
    u1 = 40
    and r = 1/2

    so --> un=u1xr^n-1
    un=40x(-1/2)^10-1
    un=-20^9
    un= -0.00000000000512
    but the correct answer is -5/256
    --> could you tell me where i got wrong?
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  2. #2
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    Hello, juliak!

    I don't agree with their answer.

    You were doing fine, then ...


    Geometric sequence: . 40,\:\text{-}20,\:10,\:\text{-}5,\:\hdots

    Find U_n and hence find the 10^{th} term.


    What i got was: . U_1 = 40\:\text{ and }\:r = \text{-}\tfrac{1}{2} . . . . Good!

    So: . U_n \:=\:U_1r^{n-1}

    . . . U_{10}\:=\:40\left(\text{-}\tfrac{1}{2}\right)^9

    We have: . U_{10} \;=\;40\cdot\frac{1}{(\text{-}2)^9} \;=\;40\cdot\frac{1}{\text{-}512} \;=\;-\frac{40}{512} \;=\;-\frac{5}{64}

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  3. #3
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    Quote Originally Posted by juliak View Post
    sequence 40, -20, 10, -5... is geometric
    find Un and hence find the 10th term

    what i got was
    u1 = 40
    and r = 1/2
    Notice the change of sign in the sequence, hence r=-\frac{1}{2}. But this is what you use then, so it must be a typo...

    so --> un=u1xr^n-1
    un=40x(-1/2)^10-1
    un=-20^9
    un= -0.00000000000512
    but the correct answer is -5/256
    --> could you tell me where i got wrong?
    This is a mistake in manipulating powers : u_n=u_1 r^{n-1}=40\left(-\frac{1}{2}\right)^{10-1}=(-1)^9 \frac{40}{2^9}=-\frac{2^3\times 5}{2^9}=-\frac{5}{2^6}=-\frac{5}{64} (I use 40=8\times 5=2^3\times 5 to simplify the ratio).
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  4. #4
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    ^ how did you get from
    40(-1/2)^9 to (-1)^9(40/2^9)
    ?
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  5. #5
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    Quote Originally Posted by juliak View Post
    ^ how did you get from
    40(-1/2)^9 to (-1)^9(40/2^9)
    ?
    The power of a product is the product of the powers: (ab)^n=a^nb^n. And the same for ratios: \left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Here, we have 40\left(-\frac{1}{2}\right)^9=40(-1)^9\left(\frac{1}{2}\right)^9=40(-1)^9\frac{1}{2^9}. Ok?
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