math

Nth expression for the following:6,11,17,24,32.....

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  1. 41 it goes up a number each time

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  2. The numbers represent the following sequence

    n........1...2...3...4...4...
    .........6..11..17..24..32...
    1st diff...5...6...7...8
    2nd dif......1...1...1

    With the 2nd differences equal to 1, the general form of the equation defining the Nth term is a quadratic of the form N = an^2 + bn + c. Using the given data we can write

    1 + b + c = 6
    4a + 2b + c = 11
    9a + 3b + c = 17

    Solving yields a = 1/2, b 7/2 and c = 2 making the general expression for the Nth term N = (n^2 + 7n + 4)/2.

    Thus, the sequence continues as
    6, 11, 17, 24, 32, 41, 51, 62, 74...

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