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For each of the following patterns, determine the rule: a. 6; 14; 22; 30 b. 2; 6; 10; 14; 18 c. 13; 10; 7; 4; 1 d. 8; 13; 18; 23; 28 e. 5; 9; 13; 17; 21 f. -20; -15; -10; -5; 0 g. 7; 18; 29; 40; 51 h.

Mathematics

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Okay, Christina, let's describe the rule for each pattern.

Part a· 1 step

6; 14; 22; 30

  1. Find the difference between consecutive terms.

    14−6=814 - 6 = 8
    22−14=822 - 14 = 8
    30−22=830 - 22 = 8
    Rule: Adding 8\boxed{\text{Adding 8}}

Part b· 1 step

2; 6; 10; 14; 18

  1. Find the difference between consecutive terms.

    6−2=46 - 2 = 4
    10−6=410 - 6 = 4
    14−10=414 - 10 = 4
    18−14=418 - 14 = 4
    Rule: Adding 4\boxed{\text{Adding 4}}

Part c· 1 step

13; 10; 7; 4; 1

  1. Find the difference between consecutive terms.

    10−13=−310 - 13 = -3
    7−10=−37 - 10 = -3
    4−7=−34 - 7 = -3
    1−4=−31 - 4 = -3
    Rule: Subtracting 3\boxed{\text{Subtracting 3}}

Part d· 1 step

8; 13; 18; 23; 28

  1. Find the difference between consecutive terms.

    13−8=513 - 8 = 5
    18−13=518 - 13 = 5
    23−18=523 - 18 = 5
    28−23=528 - 23 = 5
    Rule: Adding 5\boxed{\text{Adding 5}}

Part e· 1 step

5; 9; 13; 17; 21

  1. Find the difference between consecutive terms.

    9−5=49 - 5 = 4
    13−9=413 - 9 = 4
    17−13=417 - 13 = 4
    21−17=421 - 17 = 4
    Rule: Adding 4\boxed{\text{Adding 4}}

Part f· 1 step

20; -15; -10; -5; 0

  1. Find the difference between consecutive terms.

    −15−(−20)=5-15 - (-20) = 5
    −10−(−15)=5-10 - (-15) = 5
    −5−(−10)=5-5 - (-10) = 5
    0−(−5)=50 - (-5) = 5
    Rule: Adding 5\boxed{\text{Adding 5}}

Part g· 1 step

7; 18; 29; 40; 51

  1. Find the difference between consecutive terms.

    18−7=1118 - 7 = 11
    29−18=1129 - 18 = 11
    40−29=1140 - 29 = 11
    51−40=1151 - 40 = 11
    Rule: Adding 11\boxed{\text{Adding 11}}

Part h· 1 step

1; 9; 17; 25; 33

  1. Find the difference between consecutive terms.

    9−1=89 - 1 = 8
    17−9=817 - 9 = 8
    25−17=825 - 17 = 8
    33−25=833 - 25 = 8
    Rule: Adding 8\boxed{\text{Adding 8}}

Part h(i)· 2 steps

4; 5; 6; 7; 8

  1. Find the difference between consecutive terms.

    5−4=15 - 4 = 1
    6−5=16 - 5 = 1
    7−6=17 - 6 = 1
    8−7=18 - 7 = 1
    Rule: Adding 1\boxed{\text{Adding 1}}

    j. -6; -4; -2; 0; 2

  2. Find the difference between consecutive terms.

    −4−(−6)=2-4 - (-6) = 2
    −2−(−4)=2-2 - (-4) = 2
    0−(−2)=20 - (-2) = 2
    2−0=22 - 0 = 2
    Rule: Adding 2\boxed{\text{Adding 2}}

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