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Arithmetic sequences

  1. Nov 29, 2009 #1
    1. The problem statement, all variables and given/known data

    Find x so that x+5, 3x+1, and 4x+1 are consecutive terms of an arithmetic sequence.

    Not really sure how to do the problem at all. Some assistance would be much appreciated.
     
  2. jcsd
  3. Nov 29, 2009 #2

    Hurkyl

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    Re: Sequences

    What do you know about "three consecutive terms in an arithmetic sequence"?
     
  4. Nov 29, 2009 #3
    Re: Sequences

    Because it's an arithmetic sequence, if you add a constant to one solution you can get the next solution.
     
  5. Nov 29, 2009 #4

    Hurkyl

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    Re: Sequences

    "solution"? Did you mean "term"?

    What do you know about three consecutive terms in a sequence?



    P.S. this is algebra. Name things with variables. Express facts as equations.
     
  6. Nov 29, 2009 #5
    Re: Sequences

    Yes, I apologize, I did mean terms.
    Because the terms of an arithmetic sequence always vary by a constant
    x+a, x+2a. x+3a
    you can attain a, the constant, by subtracting two consecutive terms.
    (x+2a)-(x+a)=a or (x+3a)-(x+2a)=a
     
  7. Nov 29, 2009 #6

    Hurkyl

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    Re: Sequences

    Let's not use 'x' here! We're already using 'x' for something else!

    So we know "three consecutive terms of an arithmetic sequence" can be written as
    r+a, r+2a, r+3a​
    for an appropriate choice of r and a.

    So now, how do you express the fact that
    x+5, 3x+1, and 4x+1 are "three consecutive terms of an arithmetic sequence"​
    ?
     
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