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Conditional identity consisting of AP and GP

  1. Mar 13, 2014 #1
    1. The problem statement, all variables and given/known data
    x,y,z are three terms in GP and a,b,c are three terms in AP
    prove that (xb÷xc)(yc÷ya)(za÷zb)=1


    2. Relevant equations



    3. The attempt at a solution
    (xb-c)(yc-a)(za-b)

    since x y z are in GP
    xb-c÷yc-a=yc-a÷za-b
    (xb- c)(za-b)=yc-a(yc-a)
     
    Last edited by a moderator: Mar 13, 2014
  2. jcsd
  3. Mar 13, 2014 #2

    Mark44

    Staff: Mentor

    You are given that x, y, and z are in geometric progression. Did you use that fact in your work?

    Also, a, b, and c are in arithmetic progression. Did you use that fact in your work?
     
  4. Mar 13, 2014 #3
    got it thank you, I seem to be posting here without thinking hard
    next time I won't post without thinking out all options sorry
     
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