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Sequence Sum

  1. Oct 25, 2015 #1
    Hi!

    If I have a sequence that its first 4 terms are:

    30, -31, +32, -32

    The pattern is geometric sequence but has alternating signs..

    How can I find its sum ..

    I know it is composed of 2 sequences ..

    However, when I try to separate the 2 sequences .. I get them of different "lengths"

    In other words, it is (30+32+34) - (31+33) for 5 terms

    but for 4 terms I get:
    In other words, it is (30+32) - (31+33)


    How can I get general formula for both ..

    (-1)k helps ! but how! and what about the number of terms


    Thanks!!!
     
  2. jcsd
  3. Oct 25, 2015 #2
    Further to my previous post ..

    screenshot_158.png
     
  4. Oct 25, 2015 #3
    This is the book's answer:
    screenshot_158.png
     
  5. Oct 25, 2015 #4

    Ssnow

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    Gold Member

    When ##n## is odd that is ##n=2m+1## you obtain ## \frac{1}{4}(-3^{2m+1}+1)##, when is even ##n=2m## you obtain ## \frac{1}{4}(3^{2m+1}+1)##. In order to obtain both you must have ## \frac{1}{4}((-1)^{n}3^{n+1}+1)## (this is obtained merging the two previous...)
     
  6. Oct 25, 2015 #5

    PeroK

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    Gold Member

    If you set ##n = 1##, then your formula gives ##S = -1/2##
     
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