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17 November, 05:35

Write the sum using summation notation, assuming the suggested pattern continues. - 10 - 2 + 6 + 14 + ... + 110

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  1. 17 November, 06:57
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    This is the sum of the arithmetic sequence:

    10 - 2 + 6 + 14 + ... + 110

    where: a 1 = - 10, d = 8

    a n = 110

    a n = a 1 + (n - 1) * d

    110 = - 10 + (n - 1) * 8

    110 = - 10 + 8 n - 8

    110 + 10 + 8 = 8 n

    128 = 8 n

    n = 128 : 8

    n = 16

    ∑ n = n/2 * (a 1 + a n)

    ∑ 16 = 16/2 * (-10 + 110) = 8 * 100 = 800

    Answer:

    The sum is 800.
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