Use sigma notation to represent the sum of the first seven terms of the following sequence: −4, −6, −8, …

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Use sigma notation to represent the sum of the first seven terms of the following sequence: −4, −6, −8, …

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Jezebel 5 months 2021-08-04T19:46:00+00:00 1 Answers 50 views 0

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    2021-08-04T19:47:00+00:00

    Answer:

    \sum_{n = 1}^{7} -2 -2n

    Step-by-step explanation:

    Arithmetic sequence:

    In an arithmetic sequence, the difference of consecutive terms is always the same, called common difference.

    The nth term of a sequence is given by:

    a_{n} = a_1 + (n-1)d

    In which a_1 is the first term and d is the common difference.

    Sigma notation to represent the sum of the first seven terms

    Sum going from the index starting at 1 and finishing at 7, that is:

    \sum_{n = 1}^{7} f(n)

    Now we have to fund the function, which is given by an arithmetic sequence.

    −4, −6, −8,

    First term -4, common difference – 6 – (-4) = -6 + 4 = -2, so a_1 = -4, d = -2

    Then

    f(n) = a_{n} = a_1 + (n-1)d

    f(n) = -4 + (n-1)(-2)

    f(n) = -4 - 2n + 2 = -2 - 2n

    Sigma notation:

    Replacing f(n)

    \sum_{n = 1}^{7} -2 -2n

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )