Complete the following numerical patterns: a) 4, 8, 12, , , b) 30, 27, 24, , , c) 100, 95, 90, , , __

        $$
        8 - 4 = 4
        $$
        $$
        12 - 8 = 4
        $$

        $$
        12 + 4 = 16
        $$
        $$
        16 + 4 = 20
        $$
        $$
        20 + 4 = 24
        $$
    *   The completed pattern is $\boxed{\text{4, 8, 12, 16, 20, 24}}$.

*   b) $30, 27, 24, \underline{21}, \underline{18}, \underline{15}$

        $$
        27 - 30 = -3
        $$
        $$
        24 - 27 = -3
        $$

        $$
        24 - 3 = 21
        $$
        $$
        21 - 3 = 18
        $$
        $$
        18 - 3 = 15
        $$
    *   The completed pattern is $\boxed{\text{30, 27, 24, 21, 18, 15}}$.

*   c) $100, 95, 90, \underline{85}, \underline{80}, \underline{75}$

        $$
        95 - 100 = -5
        $$
        $$
        90 - 95 = -5
        $$

        $$
        90 - 5 = 85
        $$
        $$
        85 - 5 = 80
        $$
        $$
        80 - 5 = 75
        $$
    *   The completed pattern is $\boxed{\text{100, 95, 90, 85, 80, 75}}$.

*   a) $10, 20, 30, 40$

        $$
        20 - 10 = 10
        $$
        $$
        30 - 20 = 10
        $$
        $$
        40 - 30 = 10
        $$

    *   Rule: $\boxed{\text{Add 10 to the previous number}}$.