Negative 2 and two-thirds, negative 5 and one-third, negative 10 and two-thirds, negative 21 and one-third, negative 42 and two-thirds, elli

Question

Negative 2 and two-thirds, negative 5 and one-third, negative 10 and two-thirds, negative 21 and one-third, negative 42 and two-thirds, ellipsis Which formula can be used to describe the sequence?

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Thành Đạt 4 years 2021-07-24T22:44:23+00:00 1 Answers 16 views 0

Answers ( )

  1. quangkhai
    0
    2021-07-24T22:45:35+00:00
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    Answer:

    f(n) = -\frac{8}{3}n

    Step-by-step explanation:

    Given

    -2\frac{2}{3}, -5\frac{1}{3}, -10\frac{2}{3}, -21\frac{1}{3}, -42\frac{2}{3}

    Required

    The explicit formula

    The above sequence is an arithmetic sequence and it is bounded by:

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

    Where

    a = -2\frac{2}{3} — the first term

    d = f(2) -f(1)

    So, we have:

    d = -5\frac{1}{3} - -2\frac{2}{3}

    d = -5\frac{1}{3} +2\frac{2}{3}

    Express as improper fraction

    d = -\frac{16}{3} +\frac{8}{3}

    Take LCM

    d = \frac{-16+8}{3}

    d = -\frac{8}{3}

    So, we have:

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

    f(n) = -2\frac{2}{3} + (n - 1) * -\frac{8}{3}

    Express all fractions as improper

    f(n) = -\frac{8}{3} + (n - 1) * -\frac{8}{3}

    Open brackets

    f(n) = -\frac{8}{3} -\frac{8}{3}n +\frac{8}{3}

    Collect like terms

    f(n) = -\frac{8}{3}n +\frac{8}{3}-\frac{8}{3}

    f(n) = -\frac{8}{3}n

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