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Math Help - How to find terms in a pattern

  1. #1
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    How to find terms in a pattern

    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?
    I understand for the first step you have to find how many terms there are. Through algebra it can be determined there are 20 terms in the sequence, but I don't understand why and if this is application to any question involving arithmetic series. I know the formula and everything, but can I use the formula for every question that's similar to this asking the same question?
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  2. #2
    Member Sylvia104's Avatar
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    Re: How to find terms in a pattern

    The formula for sum of terms of an AP is

    \mathrm{\frac{(no.\ of\ terms) (first\ term + last\ term)}2}

    So first find n, the number of terms: \frac{n(3 + 136)}2 = 1390.

    When you've found n, you can find the common difference d using the formula d = \frac{136 - 3}{n-1}

    Thus the first three terms are 3,3+d,3+2d.
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