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The pattern is:

4, 8, 15, 25

Is the formula:

2.5n + 1.5n???

If you are wondering what the standard formula is, check my previous question.

Thank you! :-)

  • Algebra -

    your formula can't be right,
    try n=3 ---> 2.5(3) + 1.5(3) = 12 not the 15 that are needed.

    I do these the following way:
    the first set of differences between successive terms is 4,7,10
    and the second differences are 3,3

    so we have a constant difference in the second set, so the function must be quadratic
    let it be y = an^2 + bn + c
    from you data:
    4 = a+b+c
    8 = 4a+2b+c
    15 = 9a+3b+c
    subtract the first two: 4 = 3a + b
    subtract the last two : 7 = 5a + b

    now subract these two 3 = 2a
    a = 3/2
    sub into 4 = 3a+b --> b = -1/2
    and finally back in the first gives us
    c = 3
    so y = (3/2)n^2 - n/2 + 3

    try it, it works.

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