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Math Help - Arithmetic Series

  1. #1
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    Arithmetic Series

    In an arithmetic series, the terms of the series are equally spread out. For example, in
    1 + 5 + 9 + 13 + 17, consecutive terms are 4 apart. If the first term in an arithmetic series is
    3, the last term is 136, and the sum is 1,390, what are the first 3 terms?


    Did I do this right?


    sn=n/2(a1+an)

    1390=n(139)/2

    n=20







     increment = (136-3)/(n-1)


    133/(20-1)



    133/19 = 7



    So it'd be 3+10+17...136 = 1390.
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  2. #2
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    yes, your final series is correct
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  3. #3
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    Hello, A Beautiful Mind!

    If the first term in an arithmetic series is 3, the last term is 136,
    and the sum is 1,390, what are the first 3 terms?


    Did I do this right?

    S_n \:=\tfrac{n}{2}(a_1+a_n) \quad\Rightarrow\quad 1390\:=\:n\left(\tfrac{139}{2}\right) \quad\Rightarrow\quad n\:=\:20

    d \:=\:\frac{136-3}{n-1}\:=\: \frac{133}{20-1} \:=\: \frac{133}{19} \:=\: 7

    So it'd be: . 3+10+17 + \hdots + 136 \:=\: 1390 . . . . Absolutely!
    Don't forget to answer the question . . .

    . . First three terms: . 3, 10, 17

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