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Arithmetic means and series

  1. Sep 21, 2014 #1
    I don't understand on how to get the answer of a certain problem in arithmetic series.

    formula/s:

    Arithmetic means

    An=A1+ (n-1)d

    Arithmetic series

    Sn=n/2 (A1+An)

    I understand on how to get the terms to these but when finding for:

    Find A1 if,
    S10= -20 , d= 4

    &

    Find S12 if, 2+5+8+....

    I couldn't quite grasp the idea on how to apply the formulas to these problems.

    Any help is appreciated. Thank you very much
     
  2. jcsd
  3. Sep 21, 2014 #2
    Sn=n/2 (A1+An)

    this can also be written as Sn=n/2 (A1+(A1+ (n-1)d))

    which then further simplifies to: Sn=n/2 (2A1+ (n-1)d)

    now plug in the known values and simplify

    for your first question, the value of n=10

    for your second question,
    n=12,d=3,A1=2
     
  4. Sep 21, 2014 #3
    Thank you so much.

    So, in which case,

    Sn=n/2 (A1+An) is still equal to
    Sn=n/2 [2A1+(n-1)d]

    Just different in how to solve it.
     
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