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Sum Of An Arithmetic Series

  1. Sep 17, 2006 #1
    I'm in Algebra 2, 8th grade. This question is driving me nuts! My book and notes do not help at all.

    The sum of a series is 2125. The first term is 43 and the last term is 127. How many terms are there, and what is the common difference?

    I have no idea how to find the terms, because all of the equations I know have d in there.. and I don't know if I'm supposed to find the D first, or whatever.
     
  2. jcsd
  3. Sep 17, 2006 #2

    berkeman

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    Staff: Mentor

    What is the basic property of an arithmetic series? A constand delta between each term, right? That's probably the d you are referring to.

    So this series is (43 + 0) + (43 + d) + (43 + 2d) + ... + 127 = 2125.

    How many 43's does it take to make 2125? Then the number of terms is less than that number. Given the number of terms n, how many 43's are there, and how many d's. Does that help guide you to the answer?
     
  4. Sep 17, 2006 #3
    A little bit. So I just keep going (43 + 3d) and so on and so on? How will I finally find what d equals?
     
  5. Sep 17, 2006 #4

    berkeman

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    Write the equation for the sum in terms of d and n. Then your solutions for n have to be a whole number, although I suppose d does not have to be whole. If you get multiple solutions for non-whole d and whole n, I'd pick the answer with a whole number for both if it exists.
     
  6. Sep 17, 2006 #5
    The a(n)= a1 + (n-1)d equation?
     
  7. Sep 17, 2006 #6

    berkeman

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    No no no. Like this:

    n=3: (43+0) + (43+d) + (43+2d) = 129 + 2d = 2125
    n=4: (43+0) + (43+d) + (43+2d) + (43+3d) = 172 + 6d = 2125
    n=....

    general n: <<write the equation>>

    Then solve for several n and d to see what looks reasonable...
     
  8. Sep 17, 2006 #7

    berkeman

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    Gotta go. Good luck!
     
  9. Sep 17, 2006 #8
    thank you! i'm a wee bit closer now.
     
    Last edited: Sep 17, 2006
  10. Sep 17, 2006 #9

    berkeman

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    You're welcome. I'm just checking in from home now briefly. BTW, you will have a formula for the finite series of the sum of the multiple d terms in terms of n. That will factor into the final equations.
     
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