Arithmetic series

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  1. Arithmetic series formula
    Determine the sum of the first ten terms of the arithmetic series: 6 + 1 – 4 – 9 – … .
    1. Problem involving both arithmetic sequence formula and arithmetic series formula
      Find the sum of the arithmetic series: – 4 – 1 + 2 + …. + 329.
      1. tn=sn−sn−1t_{n}=s_{n}-s_{n-1}
        The sum of the first n terms of an arithmetic series is sn=7n2−5n{s_n} = 7{n^2} - 5n .
        1. Find the common difference.
        2. Determine the first six terms of the corresponding arithmetic sequence.
      2. A triangle has a perimeter of 32m; the shortest side is 6 m long. If the side lengths of this triangle form an arithmetic sequence, what are the other side lengths?
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        Topic Notes
        An arithmetic series is the sum of an arithmetic sequence. In this lesson, we will learn how to solve problems using the arithmetic series formula.
        • the sum of nn terms of an arithmetic series:
        sn{s_n} = n2[2t1+(n−1)d]\frac{n}{2}[2{t_1} + (n - 1)d]
        = n2[t1+tn]\frac{n}{2}[{t_1} + {t_n}]
        Basic Concepts