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Math Help - arithmetic series

  1. #1
    Senior Member pacman's Avatar
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    arithmetic series

    The fifth and and the fiftieth terms of an arithmetic sequence are 3 and 30, respectively. Find the sum of the first 10 terms.
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  2. #2
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    Quote Originally Posted by pacman View Post
    The fifth and and the fiftieth terms of an arithmetic sequence are 3 and 30, respectively. Find the sum of the first 10 terms.
    Let a_1 be the first term of the sequence and let d be the difference between terms. We know that a_5 = 3 and a_{15} = 30.

    Therefore we can deduce that since the terms are in arithmetic progression we must have that a_5 = a_1 + 4d and a_{15} = a_1 + 14d .

    We know the values of a_5 and a_{15}, so we arrive at

    a_1 + 4d = 3
    a_1 + 14d = 30

    Two equations in two unknowns, which I'm sure you can solve. Once you solve you will have a_1 and d, and you should know where to go from there. Good luck.
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  3. #3
    Senior Member pacman's Avatar
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    Pomp, excuse me, it is fiftieth not fifteenth. Thanks for your reply, i know now how to continue
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