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Arithmetic Sequence for homework,im also new to this website

  1. May 27, 2014 #1
    1. The problem statement, all variables and given/known data

    a, b and c are consecutive numbers in a geometric sequence, where a+b ≠ 0 and b+c ≠ 0

    * "/" means divide *

    Show that 2ab/a+b, b and 2bc/b+c are consecutive terms in an arithmetic sequence

    3. The attempt at a solution

    i know this has something to do with it.....

    a,b,c GP

    Show 2ab/a+b, b, 2bc/b+c .....

    T1, T2, T3 of AP

    T2-T1=T3-T2

    b-(2ab/a+b)=(2bc/b+c) - b

    b2 = ac
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 27, 2014 #2

    LCKurtz

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    If you mean 2ab/(a+b), b , 2bc/(b+c) write it that way. Parentheses matter.

    You haven't used the fact that a,b,c are a GP. That means ##b=ar^2,~c=ar^3##. Use that. Or you can divide that last equation by ab, assuming neither are zero.
     
  4. May 27, 2014 #3

    Ray Vickson

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    What you wrote means
    [tex] \frac{2ab}{a} + b \text{ and } \frac{2bc}{b}+c[/tex]
    Is that what you wanted, or did you want
    [tex] \frac{2ab}{a+b} \text{ and } \frac{2bc}{b+c}?[/tex]
    Parentheses are important: if you mean ##\frac{A}{B+C}## you need to write it in text as A/(B+C).
     
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