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Find a and r

  1. Feb 27, 2008 #1
    find a and r

    [tex]a+ar+ar^2=7[/tex]

    [tex]a^3+a^3r^3+a^3r^6=73[/tex]
     
  2. jcsd
  3. Feb 27, 2008 #2
    http://www.imf.au.dk/kurser/algebra/E05/GBintro.pdf [Broken]
     
    Last edited by a moderator: May 3, 2017
  4. Feb 28, 2008 #3
    OK but the solution where
     
  5. Feb 28, 2008 #4
    The first trial-and-error attempt I made turned out to be right: a=1, r=2,
    1 + 2 + 4 = 7,
    1 + 8 + 64 = 73.
     
  6. Feb 28, 2008 #5
    Not sure if there is more than one solution, but I found that a = 1 and r =2 works.
     
  7. Mar 1, 2008 #6
    a(1 + r + r^2) = 7

    Then you can solve for 'a' or 'r', and substitute into the other equation. It's not pretty, but it will work!

    I remember seeing a very similar problem in high school, must see if I can find it again.

    In fact, you could try by summing geometric equations.

    a + ar + ar^2 = a(1 - r^3)/(1 - r) = 7

    a^3 + a^3.r^3 + a^3.r^6 = a^3(1 - r^9)/(1 - r^3) = 73

    Divide the one sum by the other and see where it leads you.
     
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