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Homework Help: Things to expect with grade 10 Geometric Sequences

  1. Jun 6, 2006 #1
    We're going to be starting them in a day or two, and I just wanted to know ahead of time what you guys might think we'll be learning with them, like formulae and that kind of stuff..
     
  2. jcsd
  3. Jun 6, 2006 #2

    HallsofIvy

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    There's not a whole lot you have to know about "geometric sequences". A geometric sequence is one in which you go from one number to the next by always multiplying by the same thing.

    Example: 3, 6, 12, 24, 48, 96,.... The point is that 6/3= 2, 12/6= 2, 48/24= 2, 96/48= 2. In other words, you start with the number 3 and proceed to just keep multiplying by 2. If we start counting terms with n= 0 (some people start with n= 1) then the "nth" term is 3(2)n or, in more general terms, arn where a is the first term and a is the "common multiplier"j. If you start counting with n= 1, then the nth term is arn-1:you have to subtract 1 to get back to 0.

    Another nice property is this: suppose we add the terms (a geometric series rather than sequenc). For example if S= a+ ar+ ar2+ ar3, then S= a+ r(a+ ar+ ar2) where we've just lost one power. Okay, put it back in: S= a+ r(a+ ar+ ar2+ ar3- ar3. See how I added and subtracted the same thing? Now separate those: S= a+ r(a+ ar+ ar2+ ar3)+ ar4= a+ r(S)+ ar4 so
    S- rS= S(1-r)= a+ ar4= a(1- r4). That is,
    S(1-r)= a(1- r4) so S= a (1-r4)/(1- r).

    More generally, the sum of the first n terms of a geometric sequence is
    Sn= a(1-rn+1)/(1- r).
     
  4. Jun 6, 2006 #3
    Well, it seems pretty simple to me, especially after the few arithmatic formulae we've learned over the past few days. Should be fun :)
     
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