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Is there an easier way to do this question about series?

  1. Jan 29, 2016 #1
    • Moved from a technical forum, so homework template missing
    Hey guys, the question is 6.b. in the picture : http://imgur.com/FaKUMUZ
    Here is what I did to solve it : http://imgur.com/YrIvbTO
    I made these two simultaneous equations. 1875 comes from the fact that U1 + U2 = 1500 and U3 + U4 = 375. Then S4 must equal 1500+ 375(1875).
    I then found a formula for 'a' and substituted it back into S2, which I further simplified into a polynomial of degree 3 and I got the solutions r = 1, .5 & -.5.
    r can't be 1 as then the whole series would stay at whatever 'a' is, so then I concluded that it must be .5 and -.5.
    I then substituted .5 and -.5 into one of the equations and solved for 'a' which is 1000 & 3000 respectively.
    That is the actual answer, but it seemed a bit long-winded for 4 marks.
    Is there an easier way to do it? Any help would be appreciated.
     
  2. jcsd
  3. Jan 29, 2016 #2

    Samy_A

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    Set ##a_n=ar^n##.
    You know that ##a_0+a_1=1500##, ##a_2+a_3=375##.
    Replace the ##a_i##'s by their values expressed in ##a,r## in these two equations.
    They then easily let you find ##r##, and then ##a##.
     
    Last edited: Jan 29, 2016
  4. Jan 29, 2016 #3
    Yep, that worked and was much easier than my way, thanks!
     
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