Math

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Good day please help.Iam struggling with number patterns,i must fid the rule and also give the nextthree numbers in the sequence.
31;30;27,22;15

  • Math -

    look at the differences between successive terms:

    -1 -3 -5 -7

    so, the next will be 15-9=6

  • Math -

    the wonders of Wolfram
    http://www.wolframalpha.com/input/?i=pattern+%2831%2C30%2C27%2C22%2C15%29

    actual work
    did you notice that consecutive differences are
    -1, -3, -5, -7 ?
    this forms an arithmetic sequence, so a quadratic will act as the defining function.

    let the sequence be defined by
    f(n) = an^2 + bn + c
    for (1,31) ---> a + b + c = 31 , #1
    for (2,30) ---> 4a + 2b + c = 30 , #2
    subtract these two equations
    3a + b = -1
    for (3,27) ---> 9a + 3b + c = 27 , #3
    #3 - #2 ---> 5a + b = -3

    5a + b = -3
    3a + b = -1
    subtract:
    2a = -2
    a = -1

    in 3a+b=-1
    -3 +b = -1
    b = 2

    in #1: a+b+c=31
    -1+2+c = 31
    c = 30

    the defining function is
    fn) = -n^2 + 2n + 30

    (just like Wolfram said)

  • Math - thanks Reiny -

    I guess I didn't read the question too carefully, and failed to answer it fully.

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