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Math Help - find the common ratio?

  1. #1
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    find the common ratio?

    2.)The sum of a geometric series is -1023 and its first term is -3. If the last term is -768, what is the common ratio?

    please supply you work if you have the time! i would like to understand this, as well as get a good grade!
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  2. #2
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    Quote Originally Posted by lollilikeslife View Post
    2.)The sum of a geometric series is -1023 and its first term is -3. If the last term is -768, what is the common ratio?

    please supply you work if you have the time! i would like to understand this, as well as get a good grade!
    You have a number of clues to help solve this..

    Begin with the formula for the sum of a geometric series

    \displaystyle\ S_n=\frac{a\left(1-r^n\right)}{1-r}=\frac{a\left(r^n-1\right)}{r-1}

    Hence, you need three values.. a,\;\;\;r,\;\;\;r^n

    You are given "a" and two clues to find the other two values.

    S_n=-1023

    S_n=a+ar+ar^2+ar^3+......+ar^{n-1}

    hence you can find r^{n-1} using the information given for the last term.

    Also

    r^n=(r)r^{n-1}

    If you use these clues, you will get an equation in "r" which finds the value of "r".
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  3. #3
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    Re: find the common ratio?

    how to work the question
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  4. #4
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    Re: find the common ratio?

    Here is the Solution Hope this will help you,

    Given a = -3
    ar^{n} = -768
    r^{n} = -768 / -3 = 256

    so s = a (1 - r^{n}) / (1 - r)

    change the sign on rhs

    - 1023 = -3 (256 -1) / ( r -1)

    r - 1 = -3(255)/ (-1023)

    r = 1.7475 is the common ratio


    If you need to know the value of n

    1.7478....* n = 256
    n log(10) (1.7478) = log (10) 256
    n* 0.2425 = 2.4082
    n = 9.93 approximately 10
    Last edited by Sheldon; April 3rd 2013 at 10:37 PM.
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