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Math Help - Basic sum of terms equation

  1. #1
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    Question Basic sum of terms equation

    Hi
    5/3 + 15/3 + 25/3 +....(10n-5)/3 = 125/3
    solve for n

    actually i know the what answer is

    i wondering which way you prefer to solve for this

    Thanks best regards
    Last edited by blackjack21; November 5th 2012 at 02:56 AM.
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  2. #2
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    Re: Basic sum of terms equation

    sum of an arithmetic series ...

    \sum_{i = 1}^n a_i = \frac{n}{2} (a_1 + a_n)

    \sum_{i = 1}^n \frac{10i-5}{3} = \frac{n}{2} \left(\frac{5}{3} + \frac{10n-5}{3} \right) = \frac{125}{3}

    solve for n
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  3. #3
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    Re: Basic sum of terms equation

    the second term is 15/13 or 15/3 ?
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  4. #4
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    Re: Basic sum of terms equation

    Hello, blackjack21!

    \text{Solve for }n\!:\;\frac{5}{3} + \frac{15}{3} + \frac{25}{3} + \hdots + \frac{5(2n-1)}{3} \;=\;\frac{125}{3}

    Multiply by \tfrac{3}{5}\!:\;\;1 + 3 + 5 + \hdots + (2n-1) \;=\;25

    The left side is an arithmetic series with first term a=1,
    . . common difference d = 2, and n terms.

    Its sum is: . S_n \:=\:\tfrac{n}{2}\big[2(1) + (n-1)2\big] \:=\:\tfrac{n}{2}\big[2 + 2n - 2] \:=\:n^2

    Therefore: . n^2 \:=\:25 \quad\Rightarrow\quad n \:=\:5
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  5. #5
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    Re: Basic sum of terms equation

    Quote Originally Posted by pickslides View Post
    the second term is 15/13 or 15/3 ?
    sorry my fault i fixed you right its 3
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  6. #6
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    Re: Basic sum of terms equation

    thanx for the two diffrent solution better for me
    Thanks and best regards
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