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Math Help - geometric sequence problems

  1. #1
    Junior Member
    Joined
    Sep 2008
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    34

    geometric sequence problems

    Find the number of terms in the sequence

    512, -256 , 128 , ......, -1

    I got the first one correct, but i'm not sure if complete the question in proper steps due to my mistake in question two.

    tn= ar^n-1

    -1=512(-1/2)^n-1

    -1/512=(-1/2)^n-1

    -2^-9 = -2^1-n

    -9= 1-n
    -10= -n
    10=n
    There is 10 terms in total.

    Find the last term of the sequences

    the problem came out after i misdo with signs

    1/384, -1/192, 1/96, ......., -16/3

    -16/3=1/382(-1/2)^n-1

    -16x382/3=(-1/2)^n-1

    -2048= -2^1-n

    -2^11= -2^1-n

    11=1-n
    10=-n
    -10=n

    but the answer is 12 ^^;;

    i believe i made an mistake at -2048= -2^1-n..."factoring?" the -2048(negative exponents? stuck). Please check if my first problem is completed in proper steps or not. Thankyou~
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  2. #2
    Senior Member
    Joined
    Jul 2009
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    397
    Hi hovermet

    The ratio is not (-1/2)
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  3. #3
    Junior Member
    Joined
    Sep 2008
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    Ah, i see >.< the ratio is -2 thank you
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